There is no connection between Ethereum and the stablecoins on the basis of them keeping ETH alive. The Ethereum blockchain is just one of the blockchains in which those stablecoins run and without those stablecoins, ETH will exist. Likewise without the Ethereum blockchain, stablecoins will exist. Now we have more chains such as TON, TRX and others where more stablecoins are traded than ETH, yet ETH is still doing so well.
If we consider dominance then maybe Ethereum will get more dominance or demand if stable coins didn't exist in the first place, making its value rise really well, as we know that Ethereum is also a bit stable, so it should be working well as an alternative. Meanwhile, if there is stable coin that keeps Ethereum alive or shall we say more active, that will only be the stable coins that are under it because we will need Ethereum in order to operate them (you know, gas fees). Other stable coins or their creators, must still be thankful for the Ethereum and as well as Bitcoin and other cryptocurrencies because without them, there will be no motivation for them to start.