I predict that will be problematic, for at least two reasons:

(1) In a large distributed system with many transient failure modes, there can be non-malicious errors that inadvertently create double-spends. Destroying the associated value is quite a harsh penalty.

(2) When arbitrarily many followup transactions depend on a double-spent value, and then some time later the double-spend becomes evident (requiring cancellation): (a) unwinding all followup transactions is hard and disruptive; (b) future compromise of private keys would seem able to retroactively cancel true, honest transactions the holder thought had already completed before the compromise.

Very interesting. Is this based on any other consensus-finding system with any history or study behind it? Preference-aggregation/voting systems are hard.

Does this assume every provider generally knows about (and can judge the minting offers/actions of) every other?

My hunch is that the large uncertainty of supply, and potential for disagreements to leave providers confused or seeking network partitions, could prevent the necessary critical mass of stakeholders and community norms from emerging.