How can anyone and everyone prove that the tokens were actually properly paid for? Prove there were no secret smokey-room collusion deals. Prove there were no unpaid tokens minted. Prove that international government/criminal organizations didn’t blackmail a few extra tokens into existence.

You aren’t actually wrong. Tether operates the way you describe: Based on proof of Trust Me Bro :P You can build derivative products backed by Tether. But, that’s a shaky foundation on which to build a new world financial system. You’d have to hope to spin up products that earn enough trust on their own to detach their valuation from Tether before Tether collapses.