Such a certificate should not be trusted for domain verification purposes, even though it should match the domain. Instead it should be trusted for encryption / stream integrity purposes. It should be accepted on IPs outside of publicly routable space, like 192.0.0/24, or link-local IPv6 addresses. It should be possible to issue it for TLDs like .local. It should result in a usual invalid certificate warning if served off a pubic internet address.
In other words, it should be handled a bit like a self-signed certificate, only without the hassle of adding your handcrafted CA to every browser / OS.
Of course it would only make sense if a major browser would trust this special CA in its browser by default. That is, Google is in a position to introduce it. I wonder if they may have any incentive though. (To say nothing of Apple.)