I'm not sure about that, look what he did with other stablecoins like USDC, DAI, and TUSD...in which USDC is also the leading stable coin, even the market capitalization and trading volume is larger than BUSD. Until now USDT is too big to be eliminated immediately, but over time, he will also find a way to eliminate it and replace it with BUSD entirely.
Minted amount / marketcap doesn't give full picture. But BUSD has almost 200% of daily volume to USDC, and DAI isn't even in same league. I am not sure what the issue is with USDC and DAI but i am pretty sure they are going to be extra careful with stable coins after UST.
Meanwhile usdt has 334% more daily volume then BUSD. There's no competing against that. And the fact that they accept it means that people can deposit it to binance and trade there rather then elsewhere. It isn't all competition. CZ talks about going full decentralized in the future. That would mean there wouldn't necessarily be any fiat backed currency by binance.
I also don't think people will find a better and more reliable exchange than binance at this point, CZ knows that and he will take advantage of it. Currently USDT is still the stablecoin I use the most, but if I had to choose, I would choose binance over USDT.
This can all change in a heart beat, but the fact that i said that crash of usdt would crash everything goes for binance too. If binance crashes at this point, that would be something maybe too hard to recover from.