I said nothing about making it public, because I don't view the possibility of someone capturing DNS packet of the kind "A? fooserv34.hide.example.com" as making anything public. (And even if your authoritative DNS server would allow AXFR for whole hide.example.com you would only leak information that is useful for somebody who also have capability to find out the exactly same information on his own).

The convenience is about not having whatever VPN solution you use to inject DNS recursors into laptop's OS, which end ups being not reasonably solvable when you have two such VPNs you have to use at once.