> If you have unrestricted sudo [...] your password is effectively the root password.

Yes, but it keeps an audit trail of who's account was compromised, etc.

With root privilege you can erase all of the audit logs. A malicious attack probably would do so if he/she cares about that.

You can't erase remote logs, or logs written to a write-only logging device (the one's I've seen seem essentially to be a serial port/usb device that emulates a line printer).

True, but that seems tangential to the question of whether using the same password for both the root account and LUKS encryption is bad advice.