What about casino? Since it's also a third party. I've been sending funds from casino to exchange on multiple occasions and I've never had my funds frozen or asked to submit proof of origin of funds or whatsoever. Could it be that I've been fortunate all this while or exchanges main focus are on mixers?
Casinos are not privacy platforms, centralized exchanges want know the source/origin of your deposit and if you sent it through a mixer, it obscures the origin, that is they seize the coins and ask for crazy information. A casino is different as it is a gambling platform, but just to be on a safer side, you can move your money from your casino to your non-custodial wallet and then to the exchange.