why on earth would a private IP be allowed to be registered for public use?
There is absolutely no technical requirement, RFC or IETF Internet Standard or anything that requires that any public DNS record must only resolve to publicly accessible resources.
For example RFC 1537 even states:
Note that all domains that contain hosts should have a "localhost" A
record in them.
So a localhost.example.com. IN A 127.0.0.1
record is fairly common to see and 127.0.0.1 is the epitome of private IP's.
It is perfectly valid to have public DNS records that resolve to restricted access resources, to resources that are powered off, offline and/or resources that reside in an internal network. That internal network may even use RFC 1918 private use IPv4 addresses.
For larger organisations, that have an internal DNS server, populating their public DNS zone with records for resources in their internal network is usually avoided and often considered "leaking information about the layout of the internal network" and a security risk.
But for a small business or a home office without an internal DNS server, setting up printer.office.example.com IN A 192.0.2.22
in their public DNS can make life easier for everybody in that office.