If the given exchange does not require the KYC procedure to go through out, why not.
The answer is as simple as "because it isn't designed to do it". Exchanges share tons of stuff, which user owns which addresses, trading volumes, etc., with governments and chain analysis companies. As I've already shared, there's even a site[1] which takes as input an address and returns you to which exchange it belongs. It's also more expensive.
[1]
https://www.walletexplorer.com/Nice response from guy who proudly where the signature relevant to mixer which uses exchanges to snaffle customer's coin. If you could read Russian I would refer you
to real life case when user used exchange to clear his coins he got from dedicated mixer. He had to do that because those "mixed" coins where refused to be excepted by one of the service.