It's certainly an interesting round, and as others have stated, its purpose was to duplicate the performance of a 4" revolver firing the classic 125 .357 Mag round. High velocity rounds are not magic, but they penetrate barriers, like car windshields, better than heavier slower rounds. Think Highway Patrol.
Based on an earlier discussion, I had to go try this out for myself, meaning buy stuff. Both commercial (Hornady) and my loads shoot as advertised from my 4" GP-100, exceeding 1,400. The 357 Sig will too from my G23 with an OEM barrel, but it throws the brass into next week and doesn't function well. This using published loads. Commercial ammo (Federal and Speer) works well, but the Federal is going about 1,350 and the Speer just over 1,300. Someone else may get different results. Now, I know some folks are juicing their 9x19 to pretty high levels, but mine run 200 fps less than my Sig rounds, so there is some advantage. I'm still fooling with it.
But law enforcement has standardized on the .40 S&W, and some are going back to the 9. So the Sig has and probably always will see limited use. My CCW instructor was a local cop whose jurisdiction issued 357 Sig pistols. He was good with it (although at heart he's a 1911 guy), but was not at all happy about the ammo cost. He had to buy his own practice ammo.
I enjoy working with 357 Sig, but if I carry the Glock, it's the .40 barrel. And mostly I carry a small 9 mm.