Are there any advantages/disadvantages in installation/costs or anything else between the bottom door gap compared to the ventilation openings in the frame at the top?
Frame ventilation is a special component, so it also requires special payment,
the door gap is there anyway, you don't want to drag the door over the parquet or tiles,
the door manufacturer always leaves a gap there,
door width x gap height even results in a ventilation cross-section
The door frame has enough clearance in the wall opening, the gap can be as you wish or adjusted according to ventilation requirements. The door installer is also happy to come after the painter and tiler are done, so everything fits afterwards and nobody causes any damage.