So, Mixers provide service of shuffling bitcoins or provide addresses loaded with bitcoins along with private keys. In short, they provide service so to create anonymity between sender's and receiver's address so that no one can trace the transaction.
My question is why not use Exchanges? When we deposit funds on exchange, bitcoins get deposited on exchange's cold wallet. But when we withdraw funds, withdraw gets processed from exchange's hot wallet. So in short, it is very easy to do anonymous transfer by depositing funds on exchange and withdrawing to other addresses. Why to pay 1-3% fees on Mixers when it could be done for much less on Exchanges. Exchanges like Binance charge just 0.0005 BTC to process withdrawals.
The reason on why most mixers are profitable (and prohibited) are due to the fact that it provides absolute anonymity in the transactions. For example, if you were to use a mixer, the funds will be sent intermittently with necessary intervals to avoid tracking.
Exchanges, on the other hand, require you to fill details about your personal information (basically KYC). Depending on the exchange, some require personal IDs and addresses so you can increase the limits of your account with regard to withdrawal and deposits.
Although both have their corresponding transaction fees, mixers are generally higher in fees but they do provide absolute anonymity if you were to transfer funds from one wallet to another.