It's going to be particularly god-awful for devices that roam between networks where the "internal" DNS is visible and networks where it isn't. Ugh...
I don't like this one either, but often it is inherited from the past from other people and it is not going to change.
On the other hand, split-horizon DNS is going to stay with us, even if the AD domain is a subdomain of the public one. Records in the internal zone are not going to become public anytime soon.
On the other of the common problems: I assume there is no way to blackhole existing, public records, other than extension ala uBlock/Adblock?
I had thought that internal networks these days would favor multicast resolution (LLMNR/mDNS), but that doesn't appear to be the case here. Admin work is not my wheelhouse, so I have no idea what standard practice is. What is the recommended setup for AD and name resolution configuration?