If you discovered a significant shortcut to hashing and then went back to block 1 and re-mined every block until your branch was the one with the most proof-of-work, I'd have a hard time trying to claim that your branch wasn't the legitimate one, according to Bitcoin's own rules.
I suspect in this hypothetical scenario, however, the bitcoin developers would write a new rule.
Uh... yes? Are you seriously trying to imply that would be legal?
If someone ever cracks modern encryption, that doesn't mean they can do whatever they want with everyone's accounts everywhere. If you find an exploit and exploit it, that's illegal.
No, but that's not the same. Signatures and checks are covered by terms & conditions (and law) that you must follow.
A better anology is if you figure out a mathematical advantage within the rules of a casino game, are you allowed to win? I believe you are, as long as it's within the rules of the game. And the casinos are smart enough to create rules against any lasting mathematical advantage.
I know how to pick locks. The locks are designed to open when pins are raised by a certain amount. Doesn't mean I have a right to anything I can unlock.
The intention of the system is to work to as security. Just because you find a way around the security doesn't mean that you are now immune to the law regarding ownership. When SHAX gets cracked, that doesn't give the person figuring it out a right to transfer all the money out of your bank account just because they figured out the math.