There have been Microwave transformer failures from a shorted rectifier diode,cap or magnetron.They can fail.
What I wanted to say it is usually not the transformer to fail first, but very often the transformer fails as victim of the other parts failure.
Most frequently the capacitor fails as first, which then fries the diode and the HV fuse (in case of a short circuit failure). The secondary open circuit means there is no capacitive reactance load, so the primary gets overloaded by the inductive reactance current imposed by the core design (normally designed to cancel out the capacitive load nature).
Other sequence frequently occuring is the capacitor loosing capacitance, leaving extra inductive reactance on the primary so overloading it, plus the reduced magnetron power (because of the lower current feed) makes the user to operate the thing longer.
Rarely the magnetron goes away, but I've seen just one occassion and even that was more likely caused by overheating magnets loosing field because of mess accumulation on the cooling fins and on the fan.
These then end up very often by fried MOT, but can not be counted as MOT caused failures.