It breaks non-tracking functionality for embedded things on the web as currently implemented in major browsers, in particular, which is one of the largest use cases.
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.