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.