Another example is you're signed into website A, and while on website B, iframes to website A behave in such a way that you're not signed in, and you cannot sign in.
This is because the download is from googleusercontent.com while your browser remains at drive.google.com the whole time - and to download private files, googleusercontent.com expects you to have a login cookie. If you block third-party cookies the download gets stuck in a redirect loop, sending you to get a cookie over and over again.
Google is aware of this but hasn't fixed it.
It's google. I'm talking about google.
Not on iOS
1) One of my local banks (who use weird third-party hosted modules for some of their functionality).
2) Verizon.
3) T-Mobile
If I were a normal user, any one of these ("I have to do _what_ to see my FIOS bill?") could be a show-stopper.
Which is what makes it hard to turn this on by default without driving away users.
This thread contains plenty of examples of legitimate uses for third-party cookies. If FF instantly and immediately broke those, users would be cursing, not praising Firefox, and switching to a browser that doesn't break what they use.
Historically getting some browsers on board with that program has been very difficult.
Concretely: a large fraction of website developers would much rather put up "only works in Chrome" notices than fix their crap.
[Disclaimer: I used to work at Mozilla, and have done my share of trying to push for turning off third-party cookies.]
A lot of websites depends on this via auth0, cloud identity, cognito... and the experience becomes subtly broken in a way that you need to be extremely technically savvy (a developer that has a whole lot of auth experience) to understand.