Your protocol has to use a consensus mechanism if you want to reliably make progress, and be able to recover if you make mistakes, this is exactly what a blockchain solves

That you _can_ solve it with a blockchain doesn't mean that you can _only_ solve it with a blockchain.

M valid signatures of N authorities is a consensus mechanism that just needs public keys. You don't need a blockchain if you're prepared to trust a set of authorities like stripe and their trusted partners.

It's just a very unreliable consensus mechanism. Why is this being held up as a benefit?

It's not a consensus mechanism in the rigorous sense, it's more similar to a reliable broadcast protocol (less powerful)