I don't see a way in which mixers can have it easier since, they use same network as the rest of the bitcoin community. Compounding coins comes with mo advantage as, the number of confirmations would play a role too.
For deposits, the user is responsible for adjusting the fees and paying attention to the state of the network before sending to the mixer. The mixer's task can be to extend the validity of the deposit address because transactions may take much longer than expected and the sender is not able to use the RBF feature for one reason or another.
But for withdrawals, the Mixer is solely responsible for them and they must be done efficiently regardless of the state of the network if they set fixed fees for Mix operations. The only solution, in my opinion, could be to choose one of these two ideas:
1- Stopping the mixer until the end of the wave of the high fees crisis.
2- Adopting the chip method, as was done by ChipMixer, and placing the responsibility for the withdrawal on the user.