Is there a reason why all the services, that use the ActivityPub protocol don’t have a unified API?
None of the mastodon apps allow me to log in with a lemmy/kbin account.
Also none of the lemmy apps allow me to log in with a kbin account.
Even though kbin has both mastodon (microblogging) and lemmy (threads, communities) functionality.
Also, Pixelfed recently introduced “login with Mastodon”, but all it really does is just create a new user on it’s instance and copy over the mastodon followers and profile info.
Why can’t we just have one account to rule them all?
No, because the model for ActivityPub is very different than how OAuth is used for authentication. What you describe is like wanting to log in to hotmail using your gmail account, and being able to send and receive e-mail from your gmail address.
It is a fundamental to ActivityPub that a user exists at a domain, and content coming from or going to that domain is sent from / to the relevant server at that domain.
Federated login is a good idea, and it’s been done, both in closed and open forms. Combining federated login and federated ID over ActivityPub would fundamentally change ActivityPub.