That turns all users into a greater threat in the case of any bugs in the server. Makes it easier for the service to get DOS'd by authenticated users, and so on. Allowing on user to be more insecure, makes all users more insecure.
Unfortunately even privileged users (that have authority to change the permissions or possibly passwords of other users) can still use weak passwords.
A better solution would be to have your browser prevent you from reusing passwords (it only needs to keep hashes).
If the web browser is governing the passwords you can and can't have, and forcing you to have unmemorisable passwords, you're better off rethinking the whole thing. For instance, it probably makes more sense to ask the web browser to generate keypairs rather than passwords if we know the passwords cannot possibly be memorised.
I don't reuse passwords, or use a password manager. I just have a system for remembering which password to use for each website, and maintain a list of hints. And I have a pretty terrible memory. But having had the password I used to re-use across a few (non- critical) sites show up on haveibeenpwned it's what works best for me.