What "watch list"? Using ANY mixer definitely WILL put your PUBLIC ADDRESS in a watch list in a database somewhere. Using a centralized exchange could possibly do that too.
I'm pretty sure I have a list of
all Bitcoin addresses on a watch list, and I'm pretty sure there are also unused addresses on watch lists somewhere.
About WasabiWallet, OP's concern is "taint". Wasabi's developers make sure that all UTXOs that enter their pool don't come from questionable sources.
Wasabi uses a questionable source as a black list, while attacking the basics (fungibility) of Bitcoin as electronic cash.
They merely want to protect their users from taint.
I'm pretty sure they merely want to maximize their profit, and convincing people their Bitcoins are only fungible if they use Wasabi Wallet is part of that.