A decentralized algorithmic stablecoin that is overcollateralized like DAI is a demonstrably working solution. The smart contracts on Ethereum that control the DAI have sensible incentives for market participants to maintain the peg and the overcollateralization is sufficient. There is no need to trust any central party.

If a mass of transactions were sufficient, then Bitcoin would be much more stable. It is true that the USD is relatively stable not because the USG somehow "guarantees" its value rather than because the dollar is legal tender in the US. It is overwhelmingly the path of least resistance to use it for transactions in the US. The eurodollar system (international dollar denominated finance) is significant but the main stabilizing mechanism is the self-regulation of its issuance through US banks.