The most common motors on drones are brushless outrunner motors. I´ve also seen some brushless inrunner motors. Are there any brushed outrunner motors? If so, why are they so uncommon?
In general, outrunners have more torque and rotate slower than inrunners, which usually have less torque and rotate significantly quicker. The two different designs are possible because it is relatively easy to conceptualize how to flip the order of the stator and rotor within the motor due to the fact that no mechanical commutation is necessary, unlike in a brushed motor.
Almost all brushed DC motors would be classified as inrunners and very few brushed outrunner designs exist, as you note. The Wikipedia page for Brushed DC motors makes no reference to an "outrunner" brushed motor and almost no search results appear for them.
I'm not a designer of electric motors, but I have a theory for why this might be the case: the usefulness of brushed motors is mostly because they are inrunners.
The above images show "inrunner" brushed motors and the commutation mechanisms they require. If you were to make them into outrunners, the only difference they would have with brushless outrunners would be the swapped location of the coils/magnets. This setup would also increase the size of the commutation mechanism and forcing the brushes to be crammed inside the commutation ring, making it more complicated and susceptible to breaking.