Not having permission isn’t a show stopper, you will see errors in the vault’s server log saying that it can’t rotate the password, but they can be ignored.
That said, you really can’t use the dynamic secret engine to rotate your passwords as you cannot get the new rotated password out. It’s a one way vault-owner at that point.
First - The role doesn’t need permission to rotate anyone else’s credentials, just it’s own. All other users are dynamically created, then deleted when their TTL runs out.
Second - you create a user in your database that can create other users (and rotate it’s own password). Vault then logs in as that user and rotates its password, now if you need to access you ask vault to create you a temp user. Every X time, vault rotates the password for that main vault-owned user. There is no mechanism inside of vault to get the password back out. If you want to know the password you have to set it yourself in the database.