True story -
Years ago, I found a Remington 511 in a gun shop that had been poorly (at best) drilled and tapped for a scope. The gun had a nice finish on the metal and a decent stock and a shiny bore, but there weren't 3 of the 4 holes in a straight line, and none of them pointed up at the same angle. I gave it to my dad to fix all that. He soldered in some screw plugs into the old holes, then using a mill D&T'd the gun for scope bases. I did this so my son would have a decent .22 LR rifle to learn to shoot with. And the gun will shoot - half inch 5 shot groups at 25 yards are easy, with bulk ammo. Never shot any target ammo in it.
So I take my (young) son to a local range and we get set up. He's on my right and there's some of the 'shorty AR' crowd on my left, making a deafening racket (frankly I'd vote to have muzzle breaks outlawed for the nuisance they are, and REQUIRE anything with a barrel less than 18" to have a suppressor). We're all shooting at 25 yards.
My son gets bored pretty quick shooting groups so he starts shooting smiley faces and whatnot in his target. No big deal, he's having fun and I can see from his target what he's doing. Fun is what it's about.
Eventually, he gets bored at that and stops shooting and I glance over to see what he's doing. He's curious about what the other shooters are doing and is looking at their targets through his scope. The most confused, jaw-dropping look comes over his face.... and he looks at me, and the body language reads, "DAD..... what on earth??????"
Most of their targets were just random bullet holes sprayed here and there. I'm not even sure they were on paper every time at 25 yards, judging from some of this holes being near the edge of the paper. My son is in grade school and it is boggling his mind that ADULTS aren't shooting as good as him! I just shrug my shoulders and smile at him. Mind you, EVERYONE is shooting from the bench - it's required on that range.
So, if we can charitably call 12" patterns on the paper 'groups,' then that's 48 MOA 'accuracy' and I seriously doubt that lock time is playing into that. Would a trigger that breaks better help? It sure wouldn't hurt! My son and I build an AR a few years later and the trigger the gun came with was pretty awful. It has smoothed up a little over the years and is moderately tolerable. Even with that he shoots it a LOT better than those guys did. I hate to paint the AR crowd as all being that poor of skill level (some folks are getting amazing accuracy and the service rifle shooters are nothing to sneeze at), but clearly a LOT of new shooters are thinking that's the platform to start with, when they have no training or experience. I've seen it many times before.
We forget that not everyone is a crack shot, and can discern minute, theoretical accuracy nuances. I know I don't shoot enough anymore to, and for my hunting rifles, even in my best form, I probably never could have. Dunno where lock-time differences start showing up; maybe if the gun is under 1 MOA. Just guessing. Most of my bolt guns will shoot around 1MOA for 3 shots, if I'm on my game and with careful handloads. Levers maybe 1.5 MOA if I'm having a good day. ARs, to me, are difficult to handle off the bench vs. bolt guns. Lever guns are in between, as far as bench shooting technique. I've shot a gun with a set trigger - once - and that takes some getting used to. But I can see how some folks might like them.
So, if a better trigger helps someone stay on target, more than a lock time reduction will, that may be a good thing.
My ex father-in-law, since gone to the game fields in the sky, had opportunities to shoot running jack rabbits with full power rifles. He was also an excellent trap shooter. But he never could have afforded a set trigger and can't ask him anyway. He's one of the few people I've ever met that had experience shooting running game, and he'd sometimes put it to use jump-shooting deer, from the stories he told.
If I really wanted to find out whether a set trigger was more important than lock time, I'd put one on my $99 Gamo spring piston air rifle and shoot it standing for score. Even off sandbags, poor follow through shows up on target, quick! And that at 10 yards or less.