Is a switching power supply likely to fatigue or burn out early if turned on or off quickly?
Only a general answer is possible with the information you've provided.

In general, this sort of thing wouldn't be a great idea. If you had a mechanism for switching the (I'm assuming mains power) on and off that fast I'd be inclined to use it to switch the output instead of the input.

Power-on is often a stressful time for a switch-mode power supply (SMPS) due to inrush current. There would likely be less repetitive inrush current than the "cold turn-on" inrush, but the likely inrush limiting mechanism would also likely become disabled after a short run time, so that's the first risk.

The second thing I can think of is that there's no guarantee the output goes to zero immediately after input power is withdrawn. There are power storage elements in there that will generally keep things going for a while. So you might not get the effect you want without an extended off-time, and that would lead to closer to cold turn-on effects with inrush current limiting disabled. So that's thing two.

Further, depending on the supply, it might not be terrifically well behaved during start-up and shut down. There could be voltage spikes and so on which might end up damaging your LED array or whatever load you're running.

So in short, I'd say not a great idea. I'd be thinking to work on an output power switching setup right from the get-go.

If you don't mind burning up a set-up or two you could experiment to see how it reacts and maybe take some scope measurements of the voltage and current. It's possible it might work.

Are you feeling lucky? :)