I have worked for a couple of operators whose SOP's were to only utilize the radar when in the vicinity of TR's or convective activity.(or any time in doubt) I used to think this was reasonable. Perhaps it was to save the effective 'life' of the radar or a method to minimize radiation propagation, I don't know.
After several instances of almost entering or actually entering areas of non-forecast convective activity (no forwarning either), I concluded that I will always keep the radar on. I believe modern radar is much less prone to adverse radiation as well.
Aside from the obvious benefit of not being identified as a hostile threat by some military, I do not see a downside for keeping the radar on. It might save you some grief a few times in your career.