I really do not want to get sucked into this but here I go,
The 357 Sig is a 40S&W necked down to 9mm and was designed to mimic the 125 grain HP 357 mag self defence loads. It was never designed to do the hot Magnum stuff or the medium game hunting. Will it work. Yep! Was it designed for it.... Not really.
The 357 Sig is the most sucessful attempt to get to 357 Mag levels in an Auto. 38 Super was one of the first and then you have 356 and others.
Now the 40 S&W case is made by shortening the 10mm from 45 ACP length to 9X19 length to allow the 40 to be used in popular 9mm frames of the wonder 9 era (The late 80's to mid 90's) When we were given the Glock 17, Sig P226, Ruger P85, and Beretta 92FS and all of the models that chopped and bobbed those basic frames.
When the 357 Sig came out I was a big fan. I too thought it was Lightning in my hand. but really all it is, is a 120 to 150 FPS faster 9X19 or 38 super (also uses 9mm bullets) Any and all (380, 38 Spl, 9X19, 357 Sig, 38 Super, 357 Mag, 40 S&W, 10 MM, 41 mag, 44 Spl, 45 ACP, and 45 Colt) all make great self defense guns most can also be used to hunt small to medium game as well.