Most of the times when I really care about quick feedback cycles is when I'm experimenting to see what approach does and doesn't work well in the first place.

I care a lot less about it for "simple" errors like typing errors, typos, or whatnot. This is mostly trivial stuff compared to "is this entire approach good or not?"

I think I agree with you, but in trivial projects even the infamous slow compilers are fine. Toy Rust projects and small Java projects get compiled very fast.

It doesn't even have to affect compile times per se, it could be a linter/checker task running separately from the main compiler; most type errors are only relevant during development in my experience. Said experience lately is a lot of Typescript, where all type information is no longer relevant at runtime because it's compiled out or just bluntly removed to make it valid JS (I dunno how the TS compiler works).