What does the cryptography add? RIRs publish who owns which prefixes, and sign this list. If you're America worried about foreign countries hijacking BGP, you can ignore announcements received from overseas about prefixes that are owned by American actors, unless they add a record indicating they expect to deploy them overseas. You don't need any additional cryptography for this, or any protocol change.
Political routing is a faux pas. Also, not the state(s) is/are a authority.
The RIR's are. They operate a realm, and nation state and/or individual interests don't end at a border. The realm doesn't even have them.
Never the less, you are right about the need for more information being shared although it's hard to oversee what new security issues that may introduce.
You might think the state is not an authority, but everyone else who thought that got jailed by the state, so it seems to be the case that it is one. If the state and some protocol disagree, and the state has the power to imprison people using the protocol if they don't cooperate to subvert it (something like this happened to Ethereum IIRC), the protocol has to just deal with it.
It's outright crazy to see US diplomats work their ass off globally only to see some lower institution ( The FCC ) with less intelligence, capabilities, etc. undermine their work and formal US geopolitical grand strategy & policy.
