The thread here (and I mean this is summary, not as insight) appears to be the following approach.
Consider how actors lacking some previously-assumed perfection can approach that perfection in some limit (asymptotic performance / equilibrium / …). A big reason to care about such limit properties is to undergird arguments about performance in the real world. For example, the big O performance of an algorithm is used (with caveats) for anticipating performance on large amounts real-world data.
Sometimes, when we’re doing conceptual cleanup to be able to make limit arguments, we end up with formalisms that directly give us interesting properties in the intermediate stage. We may be able to throw away the arguments from limit behavior, and thus stop caring much about the limit or the formalisms we approximate there. This is the sense in which ‘the ideal fades into the background’
Yep, that’s a good way to explain it!