I don't think being a browser plugin has anything to do with it. If the problem is what mschulkind describes, then it can be fixed by changing the UI a little t

I don't think being a browser plugin has anything to do with it. If the problem is what mschulkind describes, then it can be fixed by changing the UI a little to have an autofill button while logged out, and to automatically log out after doing an autofill. I think the underlying issue, which KeePass also has, is that the entire database is encrypted. So to be able to search the database to see if a password exists, you need to decrypt the whole thing, including the passwords. If the passwords were each individually encrypted separately from the database, this could be fixed.