Fishing during the spawn (right off the spawn beds) can be an excellent method of population control for over-populated lakes. We did this alot in Texas in bluegill ponds that were stunted and over-populated.
That said, here in Colorado, fishing for bass off the beds ain't cool. Show me an over-populated bass lake here, and then I'll show you some bluefin Tuna in the Platte.
As far as trout go, I can't speak to that. Different species spawn at different times of year, so in a multi-species river or stream, it would be virtually impossible to avoid ALL spawning fish. As far as I can tell, there's no shortage of trout in this state... But like I said, I don't REALLY have a firm grasp on coldwater species' spawning habits.