But this isn't proof, that financial stock certificate. It's actually fiat: the clearinghouse or the national registry says who owns what and the court can change it.
The crypto version of proof is closer to a bearer bond or a bar of gold: whoever has possession has possession.
Yes, you pointed out why the analogy isn't perfect, all the while missing the point entirely.
In cargo cults it would be like complaining that the control tower made of wood has the wrong number of windows, all the while missing the fact that you don't have any aircraft.
If two crypto bros go to court, the one who refuses to follow the judges ruling gets to stay in jail. How does crypto help with that? Possession is 9/10ths, but the state is 100%.
The crypto version of proof is closer to a bearer bond or a bar of gold: whoever has possession has possession.