But why don't they use multiple addresses (like 10,000 different ones)? They actively reduce privacy on the entire network because of this.
Exchanges are public companies, and having more privacy means more of a burden for governments whenever they want to analyze someone's transactions. Imagine all txs from Binance came through mixers. Would be hell of a work for govs to analyze the chain - and Binance would be suspected of helping crimes.
What about mixers? How can Binance know that someone used a mixer? Of course, there is always the option of using it yourself but is that really it?
Most of the time, it's when the very recent history (1-2txs) of your address comes from a mixer. If you don't bounce your BTC from address to address after mixing the coins, the mixed transaction is so recent they'll suspect you were the person who used the mixer.