Fediverse

I am sure it was discussed here before, but I can't find a good way to search this community.

Are there any arguments against having a user's identity federate, and be compatible across platforms?

For example, let us say I sign up with my instance, matcha_addict@lemy.lol

But what if I go on mastodon, and I want to have my own micro blog. Or maybe go to write freely and post some blog posts. I'd have to make a different account on each one.

What if mastodon or write freely could just let me log in with my lemmy account (or lets call it federated account). This has several benefits:

• users don't have to scratch their head on if I am the same person or not across these platforms
• theoretically, someone following my feed can get updates on what I do on multiple platforms

Now I understand this would be difficult to implement and iron out all the edge cases, but am I missing anything on why it wouldn't be a desirable feature, given it is implemented?