There's no specific regulation that doctors can't see patients in other states. Each state simply operates their own medical licensing system. You could imagine a system that works differently, but getting there would require creating new rules and resolving new conflicts, not just removing some rule that exists today.
For example, there's a certain category of hot-button procedures that California believes are medically necessary but Texas will revoke your license for performing. To set up a shared licensing board you'd have to somehow find an acceptable compromise.
You have described every single regulatory problem anyone has ever complained about in the FDA: the default state is denial, and positive action is needed to carve permitted things out of it. If this is a categorical exemption to 'the regulations are written in blood', then you're failing to describe anything identifiable about the regulations at all.
For example, there's a certain category of hot-button procedures that California believes are medically necessary but Texas will revoke your license for performing. To set up a shared licensing board you'd have to somehow find an acceptable compromise.