I wouldn’t guess that the element heats up more when you first turn it on…it’s just that it’s going from cold to hot. When the light is sitting in it’s “on” state, it’s really flickering at 60Hz, but it’s probably so fast that the filament doesn’t cool down very much, so it’s effectively “on” full time.
I’d bet the fastest way to burn out a light would be to put it in a cycle of turning on just long enough to heat up all the way, then turning it off just long enough to cool off all the way (or most all the way). Or to shake it real hard.
I’ve heard of light bulb life extender devices which sit inline with the bulb and act as a current buffer, so that when you first flick the switch, current flows slowly, and it gradually lets more current through until it’s up to full brightness. This way, the filament heats up slowly and (supposedly) lasts longer.