If I'm reloading the jacketed slugs, is there any reason that I can't load them to .357 performance? I realize that I'll shorten the life of the brass, but will it cause any other problems?
You can, kinda, sorta. It usta be pretty common with cast. Lyman had a mould with two crimp grooves. By seating only to the rear groove, the usable volume of a .38 Special case approximated that of a .357 case and the loaded cartridge was too long to go in most .38 Special revolvers.
Second question: with the tiny amount of powder used, why is the case so large? Why can't the case be as small as a 9mm or .380 and still function to produce the velocities? Why the "wasted space"? Is it because "smokeless" hyper-heats the air in the case to propel the bullet?
Mostly for the historical reasons already cited, but the larger case generates lower pressures for the same velocity. .38 Special has been around over a hundred years, and there are pistols that old still being shot. Many of those pistols would come plumb unglued if loaded to 9mm pressures.
Another reason is that you get better accuracy with near cylinder length brass. Less jump into the barrel. PPC shooters have custom pistols built with shortened cylinders and extended barrels for .38 Special WC only. The Nagant revolvers carry this even further with cylinder length brass and a mechanism that moves the cylinder forward so that there is no room at all between the bullet and barrel at the moment of firing.
Third, and last - for now, why use a "large" primer for such a small powder load?
Been 40 years since I've seen a .357 case that took large pistol primers and those were old, then. If I ran into any, I'd junk them because they date back to the mercuric priming era. Over time, even traces of mercury can dangerously weaken brass. I'd be curious about the details of that brass. It's just remotely possible that someone did a modern run for some arcane reason.
Cartridges that are pocketed for different primers by different makers are not unknown. The 7.62x39 can be found with both large and small primers.