The problem is, that if you have an account at InstanceX, and you are browsing the website of InstanceY, InstanceY doesn’t know where your account is. I think to solve this problem, there would need to be a browser extension that knows where your account is (you configure it) and that converts Lemmy addresses to point to your instance.
Lemmy.world was just migrated to a dedicated server: https://lemmy.world/post/75556