I’d say that’s the gist of it, that we cannot “just ignore” the uncertainty because it’s too small, because if you do that then your model and the real world are indeed different. Also, at the end of it all what does “too small” mean? “Too small” compared to what? To a galaxy? To a super-nova? To a planet? To a cat? To the things we try to “discover” at CERN? To things smaller than them? To say nothing of the fact that comparing a number to physical stuff will eventually bring you head on against Zeno’s paradox, one way or the other.
I agree though that using the “too small” trick does generally allow us to do great things, like send stuff to the confines of the solar system or to build nuclear bombs, i.e. it allows us to be efficient, but that does not mean that by being efficient our models are also identical representations of what reality really is, so to speak.
What I’m saying is that maybe the “mathematization” of the physical world is a leaking abstraction, and that maybe we’d be better off by saying “we’ll never really know what the world is made up of”. But the problem is that they haven’t awarded science Nobel prizes to people saying “there’s really no way for us to learn how the Universe really works”, at least not that I know of, at best you’re seen as a mysticist when saying that, at worst as a know-nothing or a cynic.