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 always wondered what’s keeping packages back from having wheels ready the day a release drops, or way before even?
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.
It's usually a question of having the resources (usually developers to debug issues). IIRC pretty much all Windows wheels are maintained by one guy, Christoph Gohlke, he was a godsend when I worked on a Windows laptop. I owe that guy many beers.
I've never seen a better illustration of xkcd 2347 than Christoph Gohlke. I tried to find a donation link to send him small thank yous but couldn't find one.
I think the main problem is C modules. CPython only maintains ABI compatibility across minor releases (e.g. 3.10.0 and 3.10.8), so you may need a different binary compiled for CPython 3.9 and 3.10. https://docs.python.org/3/c-api/stable.html
It's absolutely an issue with C modules, especially ones that aren't easy to build or if you're running Windows where it's unlikely that there's a compilation environment setup.
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.
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).
