It's more than that, private DNS is not just a different DNS server, it's a DNS over TLS (DoT) server. This means encrypting the lookups to prevent the ISP from tracking the host names you visit.
Many DNS servers don't support DoT and some support DoH (DNS over HTTPS) instead.
they recommend leaving it on because then all your dns queries go to google and no one else by default--their "private dns" defaults to the very unprivate google dns servers.
iOS does support that.