Every service, not just mixers, definitely are incentivized to do that. That's why when people using mixers, use them behind TOR and/or VPNs, and layer your OPSEC by using other mixers/tumblers in combination with the Lightning Network and CoinJoin like Wasabi. Plus with Wasabi as the final destination of "the layer", because any UTXO that passes through your coordinator is considered "safe" by government-licensed blockchain analysis companies.
Using Tor or a VPN doesn't protect you against a mixing site,
they have full visibility over which withdrawal was claimed from which deposit.
Then that's why, layer your mixing/tumbling with other centralized mixers, then the Lightning Network, then back to onchain, then make attempts to mix them further in Wasabi's CoinJoin/centralized coordinator in order to get that "clean, safe, government-approved" UTXOs that are free from "taint".