Firstly], it should be understood that a conflict between brushed & brushless electric motor technologies had been a long-standing old trope, before the modern electric bicycle arrived on the scene. This is an old argument.
Thus, the argument (or trope) actually came into being in the relative primeval mists of electrical-technology evolution. It’s a bit like the argument whether gasoline or diesel engines are better … 20 or 40 or 80 and more years ago, the facts & particulars in play were different. The hot quiz-tip here is (as in many other technology contexts) that each type of motor has its advantages & disadvantages, strengths & weaknesses, limitations & potential. Utility brushed motors are handier, for example, if you are going to drive a homemade electric bicycle through the normal chain-gears, which is an inexpensive route. Hub-motors are obviously made to be integrated into the hub, and it’s going to be a big hassle to use them any other way. By using sprockets & chain, you can have lots of gears, which give optimum performance under a wide range of conditions, and can do it with a lower-power motor.
Brushes for electric motor commutation are today often posed as a reliability problem. Long ago, brushes wore out fast, and if not caught in time, the steel brush-holder could damage the commutator segments (which in practical terms means a motor-replacement). These problems were largely resolved, by your great-Grandpa. Today, ‘what it is’, is that brushed motors are the (much) less costly solution, and therefore market-forces sometimes create a ‘race to the bottom’, in which some specific manufactured units might be junk. But this does not appear to be a problem with bike-motors, and in particular does not appear to be a big hazard with motors intended or selected for bicycle service.
Brushes are replaceable. Because of computerized inventory & cross-referencing, virtually any brush on any motor anywhere in the world can be identified and replacements obtained, inexpensively. Now, if brush-failure has been extensive, and ignored for a long time (there is arcing, sparking & electrical burning-odors that make it obvious there is a problem), then yeah there is the possibility of commutator-damage which is not worth fixing on ordinary small motors.
Younger folks today may not know that in times not far past, electric motor repair shops where the norm in every 3-horse town in the nation. They are still common in larger population centers. The main reason these shops thrive, is that electric motors are fundamentally unchallenging technology, and everything about them can be addressed with modest investment, tooling & education. They are physically simple & manageable … FAR simpler & easier, than even a lawn-mower engine, much less car-engines.
Brushes at one time tended to wear out fast, because they were formulated to be soft and lubricating, even at the cost of reduced conductivity and increased resistance-loses. But the reason for this type of brush was mainly to spare wear of the critical copper commutater segments. Today, commutator bars are made of improved copper alloys which both improved wear-resistance and gives them better lubricating properties. Thus, brushes in turn can be made with better wear-characteristics, and do not need the lubricity that interfered with their electrical performance.
Brushes tend to wear excessively, under overload conditions. DC motors especially are