It also depnds on how short the turn-around was, on a quick turn, the brakes can still be pretty hot from the previous landing. Leaving the gear down is an accepted practise to cool them.
There is even a chart one can refer to, that given the landing distance/temp/weight, outside temp, taxi time, etc, how long the gear should be left extended after take off.
Just because I stopped arguing, doesn't mean I think you are right. It just means I gave up!