It's said that powering off and on stressed electronics more than just staying powered on all of the time. They were probably on the brink of failure, and probably wouldn't have lasted nearly as long if they were switched from the start.
The frequent switching is not a problem for the electrolytics, but rather for the resonant capacitors generating the ignition voltage: Normally they are operating at about 100V, but during start, there are many 100's of V till the electrodes warm up. And this load difference is, what cause cyclic wear.
But usually these resonant capacitors are not the limiting ballast life factor, that is mainly the electrolytic aging on just plain total burning hours, accelerated by the temperature.