No question that accuracy is paramount, but power is also a factor. Otherwise, the pros would all be carrying .22s.
I totally agree the lightweight snubbies are completely incompatible with magnum ammo. I fired 2 .357 rounds through a fellow shooter's Scandium snubbie, and returned the revolver and 3 unfired rounds to its owner. Never again ...
That said, I do carry .357 mags in my EDC snubbie, a Hogue-stocked Ruger SP101. I'm too old to be a really competitive shooter, anymore, but can consistently pass the old 5x5 test (5 rounds in a 5" circle at 5 yards, within 5 seconds, repeated 5 times). I use 125 gr SJHPs, as I believe this is the most effective round available for defensive use in this cartridge.
I carry the SP101 in preference to a lighter weapon, as I can't control this powerful round from a lighter platform. If I carry my LCR for any reason, I use .38 +P 135 gr. Gold Dots.