What you say is true for identities native to nostr. But impersonation is a real issue for people who have a reputation outside the system (we've seen this problem crop up multiple times this week). I don't know if that can be solved by binding names, because you can always create a similar name (phishers do this all the time).

A checkmark is the right idiom, but what that indicates is not that the name is bound to the account, but that the account represents the user's idea of what that name represents. The best solution I've been able to find is to show a check mark on an account when a user is following that person. Self-authenticating, so of limited utility, but at least it's something.