Before I answer that question let me give a disclaimer. I only know of someone doing this and I would personally do it myself. If you get "the gears in your cheap rotor" stripped then maybe you should have taken the advice more carefully.
By construction, just about any rotor will turn an antenna. The key seems to be having a strong enough rotor that will handle cross wind without stripping out the gears in the rotor. It is the cross wind hitting the side of the antenna that tries to turn it. if that rotor is locked in position and high winds start trying to spin it, damage could occur to the rotor.
The guy I know that is using a cheap tv antenna rotor is a very dedicated operator in a high wind area. When the storm comes he says "time to turn my antenna in to the wind". meaning he does his best to aim the pointed part of the antenna in to the direction the wind is mostly coming from. It's been holding up for quite some years, BUT, it is on a flat roof. He takes the rotor and antenna down when catastrophic winds are predicted. So as you see it depend on your install. I would not throw a beam on a tower with a cheap tv rotor.
The general point is a tv rotor will work in more of a controlled environment. It all depends all the dedication of the station owner. For example, if one had easy access to the antenna, they could build a simple locking safety device for the rotor. Remember we are talking small beam antennas here. I am saying the rotor will turn it. I am not claiming the wind won't damage it. These cheaper rotors are remote controlled. yes, that means no power cable running to the antenna rotor. Wireless Remote Controlled Rotor.