I am more familiar with the basic research phase but in my experience very few groups actually treat model choices as an engineering tradeoff. Labs usually write grants centered around whatever model organism(s) the lab is already used to, and it's rare to see a proposal that doesn't use one of a few "accepted" models. I've never seen anyone sit down and have a discussion at the proposal stage about this, to actually seriously consider alternative setups or even just acknowledge why they are choosing this same mouse again. The tradeoff defense comes after the fact, and really only if someone else brings it up.
I think it is in part a symptom of the cost of research causing labs to be centered moreso around a methodology than a question. Having some labs like this isn't a problem, but when an entire field starts to trend this way, and almost everything that gets funding chooses a particular side of a tradeoff (that isn't super well quantified to begin with), then I think we could end up missing a lot.
If you look at it another way, groups that have a handle and understanding of a particular tool may have insight into how that tool can be used to answer a biological question. I don't think there is anything really wrong with that, but grants should be denied if they aren't proposing ways to move the field forward.
There are tons of mouse labs, however some have specialized mice or mouse systems. There are also other labs that specialize in other animal systems. These systems are nontrivial to switch between for many reasons, which I think you acknowledge. It is useful for the field in general to have access to the results of a variety of research tools that every individual wouldn't necessarily have access to.
I think it is in part a symptom of the cost of research causing labs to be centered moreso around a methodology than a question. Having some labs like this isn't a problem, but when an entire field starts to trend this way, and almost everything that gets funding chooses a particular side of a tradeoff (that isn't super well quantified to begin with), then I think we could end up missing a lot.