Really good point. It would either only make sense on the same origin, or if you authenticated the domain.
It's not that what we have now is perfect, but the use-case of typing in example.com or googling example is indeed a low enough bar that non-technical users get it, and re-tooling everything to support an alternate format is a non-starter. See also: IPv6 adoption, and not many people are typing in or googling IPs.