I'd say, & hugely subjective (YE 870) kicks harder than any equivalent 12 loading, & would agree that it's probably fit more than anything else (& weight, if you throw in physics). I buy off-the-shelf & have only ever "fitted" one shotgun & that was the mentioned 20 youth stock shimming. Other than that, they fit "good enough."
A 20's great to carry 'round the field just because of the lighter weight & handier package + they'll do 90% of a 12, all told. Maybe more, as I wouldn't be totin' around my 20 for turkey or waterfowl anyway .... you pick the tool for the game.
Far as recoil, it seems to get lost somewhere in the "thrill" of the shot (to me anyways). I don't shoot competition, & actual live game is somewhat spotty - here 'n there = no biggie, so it really never comes into play regards the constant "pounding," if that. & really, what's the limit for the game afoot? 20 for doves? 3+ (or so, if you want to waterfowl), 1 turkey, those few rabbits, etc. It never mattered to me as anything pratical ....
The 20 serves plenty good enough for us "beater-types" when we don't feel like packin' the weight of as 12
Certaintly not to be anywise contradictory, but just to add a "why we go to the woods" thought. I carry a lightweight .308 "downloaded" relative to my .30-06 (for CO elk hunting) for the same reasons - it still does the job, recoil's a moot point when taking the shot - I've yet to see the lack for what I do. YMMV