The torque required to drive a positive displacement compressor is generally proportional to the pressure that it pumping against. Some induction motors, especially capacitor-run single phase ones, have a much lower start torque than maximum running torque.
What that means is that some compressors can't restart until the pressure drops. On air-conditioning compressors, it will take some time for the pressures to equalise from the hot (high pressure) and cold (low pressure) sides. If the compressor is turned on before the pressure has equalised, the compressor doesn't start and the motor will stall. In small fridges and some aircon systems, the motor overheat cutout operates. By the time the motor has cooled down. the pressure has equalised and the compressor starts OK.
Some electronically controlled systems have timers so that the motor won't overheat.
Small cooling systems have a fixed throttle, and it takes a few minutes to equalise. Larger systems have an expansion valve, and I don't know whether an expansion valve would speed up or slow down equalisation.
On air compressors, there is a similar problem. Air in the reservoir can give to much back pressure. That can be solved by having a small volume between the compressor and the reservoir, and releasing the pressure in that when the compressor stops. The compressor then has no back pressure as it starts. However, some small compressors have mechanical pressure switches that also operate the decompressor. If power is lost, the compressor isn't decompressed so it can't restart immediately. Eventually, the pressure in the small volume leaks away and the compressor can start.
I can't see how a timer could be damaged.
PS I was doing other things when writing this and Tcmtech beat me to it.