brybenn: I've seen that, too. Shooters who develop a monster flinch, after shooting a handful of heavy, 3.5" loads from a bench rest. Then, when a shot presents itself at a gobbler....invariably, they tense up, close their eyes, jerk the trigger and away goes the bird.
I went to 3" loads briefly, during the late 1980's-early 1990's. More as an experiment...to see whether they performed any better/worse than my own 2 3/4" hand loads. 1 5/8-oz/#5 copper plated shot in the 3" hull(Remington), was found to be plenty, for gobblers. These were carefully tailored loads, using Ballistics Products wads, etc. This, after extensive testing up to 2-oz shot payloads and various hulls.
I abandoned that project after a couple of years...seeing no real benefit to absorbing the extra recoil, and went back to my previous loads. Which were at the time: 2 3/4"/1 1/4-oz loads of either #4 or #5. Pretty much the plain-Jane standard "duck" load, before the advent of steel shot. No brand preference, for hull. The gobblers didn't seem to notice the change and expired with the same enthusiasm.
By the mid- 90's, I cut back the loads even further, settling on 1 1/8-oz/#6 in the 2 3/4" hull, as being about ideal(at least for me). Especially at the ranges I normally took birds. Generally, 20 yards, or less. Gun of choice: a 1923 vintage, double-barrelled Flues-Model Ithaca shotgun. Which still sees action today. Exclusively, as a black powder cartridge gun. Originally choked full/modified(more like extra-full and full)...I had the left barrel opened up some years ago, to a passable improved cylinder. Right barrel is still as tight as ever. Punches a dense, fist-sized pattern into the paper, at 30 yards.
Or, a 12-gauge Remington 870 Express(purchased in the early 1980's). The gun....like its owner, showing some dents, scratches and wear, but still functional.
The rest of the time, I like to wander the woods with a Caywood, 12 gauge flinter. Which for the last decade and a half, has pretty much put turkey on the table, every year. Or, a Pedersoli side by side, 12 gauge front stuffer. Except for those odd times when I take one or another of the other guns out, when they start complaining too loudly about being neglected.
My take on turkey hunting is this: If a shooter prefers to go with a dedicated 'turkey' gun, chambered for either a 3" or 3.5" shot shell, ...that is entirely their choice. Best of success in their hunting adventures. Just be prepared for the recoil. A hunter can also do very well with a simple single shot, double barrel, pump or autoloading shotgun and regular, 2 3/4" shot shells. I do recommend adding optics, where possible. A 1-4, 2-7 power or similar scope sight is a good choice. This makes it easier to identify birds, especially at a distance, or in heavy cover. Also aids in precise pattern placement, with tightly choked guns.