Mixing coins for privacy reasons and then using exchange is the worst idea but if you just want to break the connection between your address and coins then it's the cheapest way.

But the interesting fact is some exchanges used to mix the hacked coins using exchanges which is called chain-hopping, which involves mixing coins through stolen exchange accounts and mixing coins from BTC to Monero like privacy coins in such rapid ways before the authorities or exchanges realize something is happening but now AML procedures on centralized exchanges are tights it less likely to happen.