Flap extension (or retraction) is not a function of position in the circuit it is a function of speed. Initial flap extension reduces stall speed permitting the aircraft to fly slower while retaining an appropriate margin above the stall.
If the speed used at the end of downwind is sufficiently above the clean stall in the turn onto base then there is no requirment for flap.
The problem is that many schools use approach speeds that would not make any difference if the aircraft was clean or had flap extended.
Thus if the aircraft is slowed to an appropriate speed downwind (or at a certain distance on a straight-in approach) then flap may need to be extended.
That means that the argument should be "do you slow up downwind to a speed that requires initial stage of flap?"
Those that slag off airline ops (or those that think they are following such SOPs) should know that SOPs in airlines require a flap extension and retraction schedule to be followed. That schedule is with respect to speed. The only issue with regard to height is that departing the aircraft must be at or above the minimum flap retraction height (obstacle clearance) and on arival must be in the landing configuration (flap setting appropriate to speed and engine availability) by 1000ft.
Regards,
DFC