They actually are worried that stablecoins will take over. Right now, most stablecoins are only used for crypto trading. They seem to be pre-empting a scenario where crypto actually begins to be used on a wide scale.
I don't think stablecoins will ever take over. Bitcoin might, but not stablecoins. Since every stablecoin is based on fiat and claims to be backed up with fiat, then they all inherit all the same problems as fiat has - centralized, inflationary, seizable, not private, not censorship resistant, etc. On top of all that, you add in a further centralized third party (the stablecoin issuer), and all the risks that that brings - insolvency, fractional banking, scams, hacks, etc. Stablecoins really are the worst of both worlds. I'd rather use a CBDC than a stablecoin.
I think they are actually worried about bitcoin. It is bitcoin which has all the features they fear, and which has the widest use, widest adoption, widest user base. And after all, if they really wanted they could just seize all the fiat belonging to a stablecoin issuer and destroy that stablecoin literally overnight.