Your concerns are not unfounded, since the security of BUSD directly depends on the security of the Binance exchange. But at the same time, you should remember that BUSD aud USDT are centralized stablecoins, unlike decentralized DAI. Thus, if you are a supporter of decentralization, then it would be logical to use decentralized stablecoins.
but the DAI itself backed by crypto stablecoin like usdt and USDC as far that I know
