Another cause of burnt cylinders is prelonged climbs at low airspeeds on hot days. This will be exacerbated by engine baffles which are in poor condition, which seems to the case in many trainers. Since most trainers do not have a cylinder head temperature guage the first indication of engine overheating will be high oil temp, a lagging indicator, assuming the pilot is even monitoring the oil temp in the climb, a big assumption based on what I have seen with most PPL's....and their instructors.... By the time you see redline oil temps the cylinders will be well on their way to being cooked.
Another scenario which I think is relatively common arises from the fact that the student rarely leans the engine during their training. When they get their PPL and start going places they will lean the engine and then forget about it. Therefore if they decide to climb they wil probably just shove the throttle full in. To avoid this I make a big point in the after solo phase of the PPL that the student notes the mixture position (and indicates this to me by touching the mixture knob) before adjusting power for any flying outside the circuit. This to inculcate the habit of always linking throttle movements to the mixture setting, which will avoid the scenario mentioned above.