The 3.10 interpreter would still run 3.9-compatible Python code though, right?
Python does sometimes have backwards-incompatible changes, e.g. for 3.10 they removed a bunch of stdlib modules and methods, like the "formatter" and "parser" module [0].
So if you used those, your code wouldn't work in 3.10.
But the main reason to wait for wheels (which is pythonese for "pre-built packages") is if they use native code (like C or rust) and you would have to compile them yourself otherwise, which increases installation time quite a bit.
(this was also the reason why Alpine was a bad choice for python containers for a long time because it uses musl and there were only wheels for glibc available. AFAIK musl wheels exist now so that isn't relevant anymore)
I imagine often it’s just another parameter in a CI somewhere, where things mostly “just work” because backward-incompatible breakages have become much rarer.
However, as the page you link also mentions, a C extension may also opt to use the "Stable ABI", which does not change across major releases (with some caveats).
Pillow used to _always_ get this when a new Python release came out, because while we were generally following the betas and build away, our quarterly releases weren't sync'd with the Python ones. So there's be a gap, and every. single. time. we'd get support issues with people pip installing on the newest python and not having a compiler or the basic dependencies. (Aside: even if the last line is "Couldn't find required dependency libjpeg" many many people just don't get that it's requiring additional libraries).
So, we just shifted our fall releases to come after the Python releases.