ᐅ Bathroom vent located at floor level

We have a mechanical ventilation with heat recovery system under construction. I have now noticed that no exhaust vent is being installed in the ceiling. The bricklayers didn’t take this into account. The plumbers and HVAC installers now want to place the exhaust vent below the bathtub. I find this quite poor, as the warm, humid air rising (for example, during a shower) should ideally be extracted directly at the ceiling. Placing it at floor level between the bathtub and the toilet could also cause condensation and create a slipping hazard. Of course, they do not want to reopen the drywall. Is it even allowed to have the exhaust vent in the wet room at floor level?

I don’t think this is a good idea at all, because in case of a water overflow, the exhaust duct could also fill up. At least, that’s how I understand your point.

However, having an exhaust duct on the ceiling is manageable, in my opinion. What kind of costs would this damage incur?