The .357x125 revolver had a great reputation so they offer a similar autopistol for the Internet Age.
Not to be nitpicky but the .357 Sig was introduced in 1994. I think most would place that a few years before the beginnings of the "internet age".
The 40S&W was introduced in 1990. One of the objections to the 10mm as a service round was that the guns needed to be large and powerful ones. The first S&W guns chambered in 10mm for the FBI were larger and heavier than their 9mm sidearms. So if you could shorten the 10mm to a round that could fit in the same size guns as the 9mm did. Well they thought, you might have something. They did and it took off like a rocket.
The Sig came 4 years later and was chambered in the Sig P229. Since the idea of creating a round that would work in guns the same size as the 9mm had proven so successful with the 40 S&W... well why not do it again. The idea for it came from the 30 Luger round and efforts like the .38-45. There are two basic ways to make a round more powerful: stretch it out, but the 10mm already existed, or place a smaller bullet in a necked down case. That would work and it did. The 9mm bullet was a natural. It was heck of fast.
They could have called it the 9mm Magnum, or the 9mm Super but in an interesting coincidence a couple of fellas wrote a book promoting the "One Shot Stop" concept and promoting the idea that some of the 125 gr. loads for the .357 Magnum were better stoppers. So the name .357 Sig was easy as well and so was a promotion campaign.
But the .357 Sig languished some in the shadow of it's bigger brother. It did so for a number of years. Part of it may have been that the 9mm bullets broke up on impact at higher velocities. It did not provide better barrier penetration over what they had. It took awhile to work that out. Part may have been the bottle necked shape which, in the U.S., have never been too popular in handguns. Part may have been that the 40 was new, etc. But it did languish.
Interest in the round stepped up some after a few agencies picked it up. Seems about 2 years ago the ammo manufacturers began a major push to spark interest in it. More articles in gun mags and threads begun on gun forums.
It's a good round and needs no extra hyping, though some do, and make exaggerated claims for it. It may gain some in popularity.