Whenever you start with the "limitations" and work your way "up to" the result, you end up with a fundamentally less creative product. You can see this very clearly with people who are primarily programmers: their vision is completely clouded by implementation.
This is not philosophical idealism. I've seen this first hand. Our designers at Apple on the iPhone had absolutely no idea about hard or easy on what is arguably an incredibly more constrained platform than the web, and we made it work. We'd get completely ridiculous designs and grumble about it, but sure enough if you put the work in you could get it there. On occasion did we have to compromise and go back to them? Of course: but that is part of the process. I can guarantee that the result was better because we were forced to try everything and only change it when it absolutely didn't work. And people are surprised at Apple's great design: It's really quite simple, at Apple the designers are above the programmers, the way it should be. Its this mentality that they should be making our lives easy that leads to second rate products.
This of course displays the crux of the problem: design is about the end product, not the difficulty of putting it together. What I'm hearing is less "he doesn't understand the limitations", and more "ugh, this is going to be hard to implement, can't you just give me a dumbed down easier version of this". For years (as CSS struggled to keep up), we've heard things like "do we really need rounded corners?" "is that gradient absolutely necessary". And that's fine. I get it, there are deadlines, but we're no longer talking about being a good designer in any traditional sense, we're talking about being a good deadline-meeter (which don't get me wrong, can arguably be just as important).
But let's not kid ourselves here: this is CS we're talking about, not materials science. We're not dealing with absolute physical limitations. It's putting pixels on a screen: most of the time that I hear programmers complaining that designers don't understand the limitations, what they actually mean is that they have to resort to "inelegant" code or hacks. This of course points back to the false notion that the product is the code: it's not! The product is the website. If you have to use an image because CSS won't cut, thats OK. If you have to add hacks, thats OK. Perhaps someone looking at your code will scoff, but this isn't for them, its for the person looking at the actual website.
However, when you're working with a startup for instance, as I have had the opportunity to do for my previous few gigs, you're dealing with finite financial resources as I'm sure you realize. Talking about limitations and how long something takes to build and everything is the difference between launching or not launching before the money runs out. When you're living in that world, focusing on the limitations of the platform and finding ways to solve problems with minimal resources and in a small amount of time is often what the businesses primary problem is.
If you don't know CSS, you're not a web designer and have no business building websites to begin with. You can't design properly for a medium which has limitations you don't understand.
I don't think anyone would accept a print designer being completely ignorant of what is feasible with ink on paper, especially if you are going to be using mass-produced ink in one of various worn-in press someone else is operating.