How much additional time is needed to break a self-contained change that's the smallest it can reasonably be without breaking anything into a bunch of smaller changes though?
The question was specifically about scenarios in which this approach wouldn't work, for example because your team doesn't want to approve PRs containing only dead code or because any subset of the change won't compile or won't preserve correct behavior without the others pieces.
It helps to have the right tooling in place to ship "incomplete" work, e.g. feature flags so that you can ship a very light and not ready for end-users version of some feature, and continue to iterate on it in smaller PRs.
e.g. first pass adds a new screen and just dumps the output
IMO this is a terrible approach, and why I hate the way feature-flags are used nowadays.
For example, I'm not approving anything without input validation (frontend or backend). I have no idea if you're actually going to add validation later before the fflag is removed. "Trust me bro" doesn't work for me.