So what we learn is that funds shouldn't be deposited to a centralised exchange directly from any third party.
Judging from the two scenarios you gave in your explanation, don't you think the title of the thread is ought to have been "don't deposit funds from mixers to your centralized exchange" and not generalizing it that funds shouldn't be deposited from third party websites such as casinos and e.t.c. Because I think the major reasons why your account was restricted is simply because it was connected to a mixer, of which we know how the US government in the past few years has always been against mixers, tagging it as a tool scammers and hackers use to hide their identity after stealing funds. Because I have always sent and received crypto with my casino account to Binance and never had an issue.