The main governing body for this type of work is the international seabed authority:
A hot area they have looked at is the longing of poly metallic nodules:
While no one has actually started mining operations yet, they are working in that direction, trying to get ahead of the environmental impacts first and foremost.
While there is a strong argument for “protecting” the environment, I don’t see that as a justification in it if itself to not do resource extraction. While not perfect, they seem to be heading toward a conservative approach to mining. In it (at least last I heard) they are deliberately setting aside large swaths of areas with the valuable resource as “wildlife reserves” similar to what we do in the United States, and Australia is going for the Great Barrier Reef.
I don’t know the future here, but there are too many people in this planet clamoring for resources not to look at all options (though personally I would prefer to enable space mining).
Or have been pressured into silence.
There's no argument that environment impact needs to be evaluated--that's just not what these particular people are qualified to assess. It's unlikely that the entirety of academia will avoid discussing the potential consequences of these ideas. Those who are qualified to do so will.
a) commerical fishing, since you are disrupting the ocean ecosystem in a big way
b) probably accelerate global warming by leading to CO2 release from carbon sequestered on the floor 
The first point is easy to explain to anyone, even if they don't believe in anthropogenic climate change and refuse to see the dangers implied by the 2nd..
(Longer, more detailed version) Early in our evolutionary history, when we were still unicellular organisms, we absorbed another life form that came to live in symbiosis with us. Mitochondrion are like cells inside our cells. They reproduce and are transmitted through the mother. They code for a few proteins we need to survive. Their malfunctions is believed to play a role in some degenerative diseases such as Parkinson or Alzheimer.
Unfortunately, they did not evolve the same complex self-repair mechanisms that our nucleus did. A lot of factors cause mitochondrial DNA to degrade. This gave an evolutionary incentive to find ways for the nucleus to encode genes for similar proteins so that less functions may be impaired by mitochondrial development.
It can't be the same gene though, for reasons that are a bit complicated. As a summary let's say that the membrane of mitochondrion is easier to cross that the one of the nucleus, so you need a kind of shape hack to get it through. Imagine that you are asked to copy a vehicle, but the copy also has to be able to unfold in a way that allows through to go through a manhole. Not trivial.
Luckily, the pressure to find these genetic recipes exists in all the eukaryote domain, which includes all the animals and the plans (and a few other things). That includes a huge number of organisms that we have never sequences or even named. Recipes that work for their nucleus has a good chance of being able to work with ours. So far we found recipes for 6 of the 13 genes we need, but every time a species disappear without us being able to check for these, we may be kissing our ticket to eternity goodbye.
These 13 genes are vital, but I must also add that every gene in living organisms is a recipe for a useful molecule. Remember that spider silk has a higher tensile strength than steel, and that we know next to nothing about organisms that survive in high pressure environments.
Killing species for short-term resources is as dumb as uncovering an encyclopedia written by advanced aliens and burning it for heat.
Could we somehow find these genes through simulation? Unlikely. The protein folding problem is a n-body problem and a billion years of evolution did not find a smarter way than brute force to solve it. And by the way, it ran a brute force algorithm on a billion year in a lab the size of a planet. Realize the incredible value of this rainbow table.
Really, even if we do not care at all about biodiversity on the philosophical level, we should care about it on a very egoistical level. It is likely to be the most precious thing our planet contains: solution to uncomputable problems.
The primary function of mitochondria is the production of ATP which is then used for energy throughout the rest of the cell. Protein coding by the mitochondria, I would guess, is just a way that this very important part of a cell can have a more powerful feedback loop with the rest of the cell. Unless we can create some kind of nano-bot replacement for the creation of ATP in the cell, with all the right feedback loops, etc., just coding the proteins that the mitochondria codes for in the cell DNA will not work at all.
Experimental treatments are always expensive. Once you industrialize them, they become cheap. And it turns out that aging is a pretty common disease that many people would be ready to treat.
 In yesterday's NYT: https://www.nytimes.com/2019/01/10/climate/ocean-warming-cli...
"A new analysis, published Thursday in the journal Science, found that the oceans are heating up 40 percent faster on average than a United Nations panel estimated five years ago. The researchers also concluded that ocean temperatures have broken records for several straight years."
It's really disturbing.
There's a lot of fish (and other animals) in the top four meters, a lot of others in the forty meters below that, and somewhat less in the layer below that, but once you get to kilometers of depth things change. There are many species still, but fewer individuals of each species. Life also slows down — animals down there grow slowly and reproduce late.
I personally don't like to mine down there. We should make our mess where we can get to it, and can clean up any problems. But conflicts with fish aren't likely to be a big problem. Driving some rare species into extinction, perhaps releasing a bunch of contaminants where we can't clean up and don't know where they will flow, yes, both of those, but not conflicts with the rich fisheries near the surface.
"Bottom trawling also stirs up the sediment at the bottom of the sea. The resulting undersea plumes of “suspended solids” can drift with the current for tens of miles from the source of the trawling, introducing turbidity throughout the water that inhibits the transfer of light down to the depths where it is needed for photosynthesis in plankton, sea kelp and other undersea plants that serve as the basis for the marine food chain. Also, ocean sediments serve as natural safe resting places for many persistent organic pollutants (such as DDT and PCBs). Dredging these sediments up effectively reintroduces such toxins into the water where they are unwittingly absorbed and consumed by the fish we eat and other marine life already trying to cope with otherwise compromised undersea habitats. The sediment plumes also reintroduce nutrient solids from agricultural and other practices, increasing demand for oxygen in the water (causing algae blooms) and contributing to the outbreak of ocean “dead zones” devoid of marine life." 
And of course there are comercial species of very expensive yummy crustaceans living there. A couple of trawls and all is lost for the next thousands of years.
What we do on the surface has far more effect on these species than does the researchers' mud-digging at far greater depths.
Actually even Lophelia should be considered in the category "too deep to worry about", because as you pointed out they don't photosynthesize. They don't interact with us, and they don't interact with anything we interact with.
First of all, you are forgetting that all corals are pelagic species.
The "too deep to worry about" and "don't interact with anything we interact with" is also wrong both as concept and also as fact.
Lophelia reefs are the coral reefs of temperate areas. Can be found between 30 and 3000 m deep.
Until relatively recent times, we didn't even knew that we have coral reefs in UK, Norway or Canada. Still we don't know a lot about this places, but coral reefs are among the most rich ecosystems in the planet supporting an astonishing amount of biodiversity. As any other reef we know that they provide refuge for a (still poorly know, but probably very high) number of crustaceans, other invertebrates and fishes. It seems that Is an important refuge for sharks for example. Sharks play a role in keeping healthy marine ecosystems.
Next Cape Cañaveral growths a similar (much shallower) cold reef in a relatively narrow band that was the first marine area closed for research in USA. The Oculina Bank area of particular concern. Many fisheries depend on the Oculina reef. Their damage was directly linked with the demise of Florida's grouper fisheries for example.
We are also also slowly understanding how complex are soft bottom ecosystems. Much more complex that we previously though. Under the silt there are the equivalent of fields of grasses and shrubs but carved on negative space.
Is not just sand, is also 4000 years old antipatharians, is really smart predators that hold the key to made robots coated in one of the most resistent bio-matherials known in the planet. One that is able to stand high pressures, but that is also light, and that can also generate ultra-fast movements enduring well the mechanical damage
In silt bottoms we can found animals able to literally make the water boil around them. They can raise the temperature of a tiny amount of water to around 4000 degrees C. And they can do it in less than a second. Not, I'm not joking.
And there is also the "too deep to worry about" and "don't interact with us" small Aequorea, that blew our minds and changed forever how we, humans, do modern biosanitary research in the entire planet.
Lots and lots and lots of valuable things for humans.
Let's pay the tremendous up-front costs of lifting mining operations out and reap the long (caveat: very long) term benefits of doing so.
edit: In case that came across as sarcasm, I am in dead earnest. Whatever the relative costs of so-called asteroid mining versus deep sea mining, the ecological cost tips the balance waaay in the favor of asteroid mining. It's just that we'd have to have a longer-term mindset than we currently do.
seriously, whatever the (overstated, imo) danger of moving mass into Earth orbit is, it can be mitigated - and probably a lot more easily than the dangers of deep sea drilling can be.
Perhaps this is why China wants to build a moon base
Of course, it's still likely that the costs involved mean this idea wouldn't work in today's market conditions. That doesn't mean that conditions would never change...
Across all materials from coal, diamonds, salt, copper, etc it all adds up to just ~600billion per year in revenue and profit margins that jump all over the pace from year to year.
PS: Rare earth minerals are also generally discarded. It’s the effort to remove them from ore that’s the issue not finding them.
The kind of thing that kind of makes you second guess the "whacky" conspiracy crackpots.