Bathroom exhaust at the floor

We have a controlled residential ventilation system with [WR] under construction. Now I have noticed that no exhaust air is being installed in the ceiling. The masons did not consider this. The sanitary and ventilation installers now want to place the exhaust air outlet underneath the bathtub. I find that quite poor; the moist warm rising air (e.g. when showering) should be extracted directly at the ceiling. At the floor between the bathtub and the toilet, condensation could also occur and lead to a slipping hazard. Of course, they do not want to reopen the drywall. Is exhaust air at floor level in the wet room even permissible?

I don't think that's a good idea at all, because in the event of water overflow, the exhaust duct can also fill up. At least that's how I understand you. A corresponding exhaust duct on the ceiling is tolerable, if you ask me. What costs does this damage entail?