...they already had the round of the full potential of the time...the .38-44 also known as the High Speed...it's all they could get out of the .38 Special case with the powders of the time.
As to why the .357 Magnum and why only in the the N-Frame...
1) NEW GUN SALES! S&W had bragging rights to the most powerful handgun made...
2) RECOIL!!!! Anyone here like shooting full load .357s from Js and Ks?
Only reason that the mid size .357s came about was the *****ing and moaning from LEOs who didn't like carrying N-fames and New Service size guns. And rarely did any department require them to qualify with full charge .357 ammo...it was all waddcutters. When liability issues came up when it was discovered that officers were not qualifying with what they carried and had to change...the Ks shook apart and the Ls came to be. Which is why Ls have full underlugs...recoil control.
The 38-44 was definitely not loaded to the full potential of the 38 Special. The Keith load of 13.5 grains of 2400 under his 173 gr. LSWC was way more powerful, and that is what led S&W and Winchester to pull the trigger on the 357 Magnum. The ammo companies made the 38/44 right alongside normal pressure 38 Special. They drew the line at Keith's loading and insisted on making it impossible to load that into any old 38, hence the 357 Mag.
1) This is not the reason. The new cartridge was seen as too powerful for existing guns and they built it on top of the 44 frame which later was named the N frame.
Sales were definitely another benefit, although the first 357s were extremely exclusive and rare items, and VERY expensive. They discontinued the program in only a few years when WW2 hit. Only a little more than 5,000 were built in the 5 or so years of the program.
2) Tons of people shoot 357s today from J's and K's. J's didn't even exist in 1935, and like I mentioned above, K's were thought to be too light for the new cartridge in terms of strength and holding the gun together over the long haul.
You're right about the new guns in the 50s. Bill Jordan wanted a smaller, handier gun and the Combat Magnum was created on the K-frame. You're also right that they used light loads most of the time. When they went to full charge loads for practice in the 70s, this is when they started seeing cracked forcing cones, etc. Obviously durability was still a concern by the 50s.
But I'm not sure why you wouldn't think the K's of the 30s wouldn't have shaken apart as you indicate the later K's did. Durability WAS the concern which is why the N fame was used in the 30s. And you're right, it's why the L frame came about! It solved the problems of the old K frame guns when it came to durability with full power 357 Magnum rounds.
This article answers lots of these questions:
GUNS Magazine Handloading for Medium and Large Frame .38 Specials - GUNS Magazine