So the point is to use the stateless currency, but continue to rely on the state to settle disputes and redistribute funds as it sees fit?

That seems counter to the ethos of the BitCoin enthusiasts.

I also doubt it will necessarily work for large sums. Governments may enforce contracts related to foreign money (if they find that the contract itself is in their jurisdiction, which isn't always the case) because they have quid pro quo agreements with other states, and it is mutually beneficial to global trade if global contracts can be enforced. (In a way, it similar to foreign mail being carried by local postal services.) But there is no quid pro quo with any friendly BitCoin government, so there is no incentive to enforce contracts.