And since restoring from paper generates the same wallet, it will still work.

Be careful about putting a password on the paper backup.  One of the main uses (perhaps the main use) of the paper backup is to recover from a forgotten password, so if your backup is password protected, you are lost.  Unfortunately, one can no longer assume that the burglar is ignorant about bitcoin, so consider generating a 2-of-3 paper backup (any one backup stolen is useless to the thief, but if you lose one backup, the remaining two are enough to recover your wallet).