You shouldn't because a filesystem snapshot should be equivalent to hard powering off the system. So any crash-safe program should be able to be backed up with just filesystem snapshots.

There will likely be some recovery process after restoring / rollback as it is effectively an unclean shutdown but this is unlikely to be much slower than regular backup restoration.

Nope, CoW is wonderful. Postgres will start up in crash recovery mode if you recover from a snapshot, but as long as you don’t have an insane amount of WAL to chew through, it’s fine.