If we think about stability from first principles, then when you're talking about aggregating up billions and trillions of transactions, each of which occurs with some characteristic frequency, then the primary factors are coupling strength (how correlated or uncorrelated are those frequencies?) and bandwidth (how wide is the spread of their characteristic frequencies).

It's very popular right now to look down on the central banks for the inflationary influence of monetary policy. Less well appreciated is their role in damping volatility through decoupling (by calming herding behavior -- e.g., stopping bank runs) and increasing bandwidth (by offering the longest terms of credit and the ultimate put).

I believe you have to look all the way back to how market panics were resolved by J.P. Morgan (the person) to get a sense of how volatility in a internet-native stable coin might be addressed. I love crypto, but I don't see that crypto has fundamentally changed human nature, which means that ultimately some crypto holder will have to serve as the liquidity provider of last resort. This, in turn, raises all the same questions about centralization vs. decentralization and democratic values that we have with respect to the central banks in terms of how they handle monetary policy.

But maybe there's a way I haven't seen yet.