Because the back-up revolver would be a last resort weapon, you'd want as much stopping power as possible, and it would be deployed only at a very close range, why wouldn't .357 Magnum cartridge be better and preferred by more?
SHORT ANSWERS
1. Because your premises may not be valid.
2. More times than I'd like, my J-frame is my PRIMARY firearm. Sure, I like to pack my 1911 GM in .45ACP, but that does not always happen.
3. You can still miss up close. Just look at the MANY stop&rob videos where many shots are fired at arm's length, but no one is hit and everyone is able to walk home to change their soiled breeches.
4. You may have to make a long(er) range shot or have to hit a small(er) target and hope to hit. The scenario we expect may not be the scenario we get dealt.
5. What was that you said? I can't hear you because I just lit off a .357mag 125gr pill in my snubby whilst being attacked in a tight corridor and I now have nigh-unbearable tinnitus and permanent hearing loss. And the recoil of that .357mag made my arthritic hand nigh upon useless for the next week, when I will finally be able to make that follow-up shot.
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FAT CHEWING
I will cut to the chase and say that I used to--before age and injuries caught up to me--stoke my snubbies with .357mag JHP or my .38spl with hot boutique +P 158gr HP. I could shoot it well enough for my purposes.
Nowadays, I feed my snubbies standard pressure semi-wadcutters & target wadcutters.
In general, choose the ammunition you can shoot well enough in your chosen J-frame to meet your requirements for accurate hits at your chosen distance.
That ammo may be different for your all-steel snubby relative to your Airlight titanium/scandium snubby. Just look at the weight differences below and reflect on Force = Mass x Acceleration or Acceleration = Force / Mass.
General SW J-frame Categories
*All-Steel
Steel frame, steel cylinder
~22oz
*Airweight
Alum alloy frame, steel cylinder
~15oz
~
*Airlight
Scandium/Alum Alloy frame, Titanium Cylinder
~12oz
Ammunition for J-frames
Lots of good ammo out there, nowadays, from mild to wild. I have packed most sorts, from hot .357mag hunting loads to target wadcutters for good reasons at the time.
.357mag in Snubby Revolvers
Yes, .357mag out of a snubby is significantly more powerful than .38spl +P. There is velocity loss from a 2" bbl, but .357mag is a mad man relative to .38spl.
*.357mag Hunting
Usually 158-180 grain, hard cast or controlled expansion HP. Worried about 4-legged threats, but don't want to pack a big revolver? Here you go. If you can manage the subjective recoil and muzzle blast. Oddly enough, easier on the shooter than hot 125gr .357mag. Winchester 180gr Partition HP was ridiculously accurate out of my .357mag snubby. And POA = POI at the ranges I cared about. Freakish and people will look at you funny if they learn you are packing serious anti-Bambi/Simba pills in your snubby. Penetration? Oh, yes.
*158gr JHP/SJHP
If you can manage the recoil, this will work like gangbusters, with less pain than 125gr. And you don't need some sort of premium hollow point. There is enough velocity for ancient JHP/SJHP to open up and wreck a human. Penetration is not excessive.
*125gr JHP/SJHP
The pinnacle of .357mag snubby pain and muzzle blast. You want some elbow room at the indoor range? Light off some of these outta your 640/649 and your neighbors may well pack up and come back another day. Recoil is vicious. Muzzle blast the the shooter is awful. Muzzle blast for someone standing next to the shooter has to be experienced. I shot these, never carried them. Too much like holding on to a firecracker on a dare. Or catching a fastball without a mitt. Terminal effect of 125gr .357mag is legendary. Penetration is not excessive.
*110gr JHP
Not too familiar with these, but hear while they wreck the target, penetration can be lacking. Never shot them. Try some, tell us about it.
*"Short BBL" or Reduced Recoil .357mag
Usually 125-135gr premium pills. They work. Still much recoil to manage.
.38SPl +P in Snubby Revolvers
*Heavy 158gr JHP +P
Generally, don't waste your time. HEAVY HP won't perform out of a snubby. Get LRN effects.
*FBI Load (+P 158gr LSWCHP) from big Ammo makers
Don't waste your time/money/recoil on them in a snubby. Not enough velocity out of a 2" bbl to justify the extra recoil of +P, as most likely the HP will not open reliably, given so many jello-warrior tests. Get LRN effects. OTOH, this is my chosen SD/HD load in my 4" bbl .357mags.
*Hotter FBI Load (+P 158gr LSWCHP) or 158gr JHP from boutique ammo makers
Such as Underwood or Buffalo Bore. They squeeze out enough velocity to open up the HP to possibly make them worth the recoil. If you can handle the recoil, this is good stuff.
*Lighter JHP +P (110-135gr)
Generally, the better premium selections of these work as advertised, especially the "Short BBL" and Treasury Load variants. Penetration can be spotty.
.38spl Standard Pressure from Snubbies
*Most any HP/JHP
Just not enough velocity to get any of the JHP to work. Maybe the old Nyclad was an exception. Generally, don;t bother as they will act like LRN, so seek increased effectiveness with more meplat.
*Lead Round Nose (158gr)
Called The Widowmaker for a reason. Mild recoil.
*Semi-wadcutter & NON-Target Wadcutter (148-158gr)
Good penetration, damage IAW meplat size. Mild recoil and muzzle blast. Some of the hotter choices are good woods carry rounds. SWC good for reloads for those that pack WC in their cylinder.
*Target Wadcutter (148gr)
.38spl snubby shooting on Easy Mode. After a workout with .38spl +P or .357mag, you will wonder at how easy it is to hit the target with these and quick follow-up shots. If you have an injured limb (in the fight or maybe a chronic condition) you will appreciate these. Penetration is good and damage commensurate to the meplat.