People talk about things like Bitcoin as a threat to sovereign currencies, and they are, as competitors, of sorts. But stablecoins are another matter entirely. One huge aspect of the value of sovereign currencies is that they are instruments of law -- courts will settle in them as a lowest common denominator, and it is safe to use them in all sorts of settings as a result.
When dollar-denominated assets appear, they always run the risk of being considered a dollar-equivalent. For example, bank deposits are dollar-denominated, and are considered dollar-equivalent (even dollar-superior, in the sense that there are transactions that you can't legally do with specie, only with bank deposits, like buy stocks). That means that if banks (which are businesses) are not good at doing business, the government is essentially forced to treat them as dollar-equivalents by making them whole. See Savings & Loan Crisis, the GFC, LTCG, etc., etc.
Stablecoins piggyback on the legal aspects of dollars, and as long as you treat them as dollar-denominated assets, you're fine. The second you treat them as dollar-equivalents, you run the risk of a change in the value of that asset being something that the government is forced into supporting.