First I think the 357 Sig is the only interesting "alternative" cartridge"(10mm, 40 and the infamous 45 gap). Those others offer nothing a 9mm doesn't (and I though in 45 as its no more lethal than a 9mm)
While there was potentially some rational for the splitting of the semi auto calibers, in reality with the SD ammunition that came along about the same time it turned out to be no gain.
So, most of the following details apply to the .40, 10mm and the 45 gap. None offer anything special in that they change the equation that you have to have good hits and usually multiples to work.
The 357 Sig real niche would really be Highway Patrol. There (and other specialty units) where there is barrier penetration needs regularly, it would be the logical choice
I had to laugh that we had a trooper up here shoot an aggressive dog with his .40 right in the head and it did not kill it. Supposedly the Virginia HP moved to the 357 due to that reason (from their 9mm).
Feeding would be theoretically better but again that’s not an issue with modern semi autos.
I am looking at a pure range gun eventually and the 357 Sig is the caliber I will get it in. I can use any of the 9mm bullets and I reload. So its more an interest and a change thing that anything more effective (though its gotten a reputation for being accurate)
It certainly can be an effective HD gun (downloaded as barrier penetration is not what you want there)
And you can guess that glock which drives a great deal of the police market (Alaska State Troopers included sadly) with their "deals" is not going to offer up freely the 357 Sig (they will not put the SIG on the gun now) to anyone. If they are forced to yes, but offer no.
For LEO to make a major change is not likely due to the current investment (both political and cost they spent convincing the power that be that they had to go to 40.)
Its really a shame. Coming sooner it would have been a better in between round that the .40 or the 10mm, but then that’s how it goes.
We can enjoy it. There may be a slow shift to it for LEO in some departments over time as it proves to be more effective (mostly Highway Patrol). Either a time to reequip or enough failures of the shooting types that they decide to shift.