Dropbox, Facebook, Google, GitHub, GitLab, even Login.gov works fine with multiple tokens.

More sites should do WebAuthn (you should not do greenfield deployments of U2F today, WebAuthn is the standard). Yes, AWS should fix their feature but that shouldn't block the next ten would-be Unicorns from doing WebAuthn.

Usually you get a UI where you can add new ones and remove old ones, and when you add a new one you name it in their UI so that you can tell it apart from any others.