I don't think it is just about mice though- it is also about "pure bred" anything. Imagine there was a single human that we could do all kinds of knockout experiments with, but we would always be starting with that base human (and on top of that it would be inbred and always live in the same kind of environment). Some of the conclusions we would draw would certainly not extend to all humans, probably not to most even. If the entire field became centered around this human, we would be missing huge amounts of information in space we are not exploring at all.
Controls are great, and it makes perfect sense to have studies that produce these extremely well controlled results. But controlling does have its own tradeoffs in practice, as results may very well not be robust/not generalize to things we care about. My problem is that the entire system operates under essentially the same paradigm, so we have very little work trying to address these downsides.