Flinch control is just one reason for reducing loads. It's the cheapest way to recoil recoil, but you're handicapping yourself. As my friend Big Jim opined, a light load will break a target, but he neglected to mention that a full load will break it better. Most competitors use the maximum amount of shot allowed.
Kick and flinching can be a problem for some. I know several competitors who have a higher average with a 20-ga than a 12-ga. This is usually because they are shooting an unaltered gun. Some folks can wear clothes right off of the rack and others need theirs altered -- the same goes for shotguns.
I can shoot my main comp guns all day without any ill effects. Yet, this was not the case when they were new, they beat me up. I tried it all with my guns: hi-tech recoil pads, longer forcing cones, over-bored barrels, porting, mercury filled recoil reducers, slower burning powders, and sissy loads. Each made some degree of difference; but, for a quantum reduction in recoil, a proper fitting stock with a recoil reduction device is hard to beat. With a JS system on my Skeet gun, and a Shockmaster on my trap gun, my 12s shoot flinch-free. YMMV.
Using reduced loads, or a smaller gauge, can be a practice aid that helps you get bettered centered on the targets. Most of my practice rounds are with small gauge rounds. Another reason to use reduced loads is for quicker acquisition of a subsequent shot. In doubles events, I use a lighter load for the first shot and a standard load for the second target.
Using reduced loads is more economical for the loader. If you're a reloader, you know the most expensive component is lead, be it in slugs or shot. If you shoot factory reduced loads, you're giving the factory more profit.