The systems that execute the code for and track the values of stablecoins are themselves networks that only work because of consensus systems designed around a cryptocurrency incentive. So if you want to be able to send some large amount of USDC you need some small amount of ETH or MATIC or AVAX or whatever to pay for the usage of the shared ledger, and that's where these cryptocurrencies then get their underlying value.

Why would one expect Bitcoin which is more-or-less trying to disrupt the world order to be stable at this point in its evolution? Maybe in 20 years it'll be stable, but now? Sort of like saying that there was political instability in US following the revolutionary or civil wars and that therefore the US would never be a country that could be depended upon for international trade.