From what I gather, the Mormon church has a very complex and well developed infrastructure for deciding who gets help, what kind of help they get, etc. This seems unlikely to be readily and easily replicable without the Mormon church. It has nothing to do with whether or not one believes in god. It has to do with social infrastructure.
A government agency could eventually build the social infrastructure (though they might make a mess of it). But building the consensus that we're going to solve this problem, even if it costs us a lot is... difficult. As you said, probably not reproduceable elsewhere.
I'm a non-Mormon living in Utah. I don't praise the Mormon Church very often. But on this I think they have done well, to have the desire and willpower to address the issue.
Though, to my mind, the willpower and desire is part and parcel of what I am talking about when I say social infrastructure. That sense of community and social responsibility etc is something we tend to see closely tied to religious groups and tend to not see to that degree for, say, government run social programs.
*former Latter-day Saint
>used to cut the welfare checks under congregational leadership
You mean, send people to the storehouse as part of the Bishopric? It's pretty rare for people to be given money. Food from the storehouses yes, work through Church-owned companies and help via job placement services yes.
At least around here, maybe it's different in SLC.
"Who can help bro/sis so and so" or in EQ "So and so is looking for part-time work if you know of any place" and being sent to the storehouse for food. A friend was told no financial assistance and that she should consider subletting one of the rooms in the house she rented, even though there were 3 bedrooms for her and 5 kids and then 'coincidentally' within a week after that she had family services in her house saying she had x days to get a functional refrigerator before her children would be taken (apparently that's a thing). People here will ask for help on the private FB group for the ward when they do occasionally need it.
I imagine you see more instances because you probably have a considerably larger ward. We don't even set up overflow most weeks and I'm fairly certain in 13 years I've had to share a pew less than 5 times for sacrament and even at tri-stake mid-singles firesides we have tons of empty pew space.
With regards to referring to the Mormon church as Mormon: I will use the common reference standard as it will likely be returned to in a few years. The whole recent re-labeling is useful internally but not my business externally.[0] Not my rodeo, not my clowns.
[0] https://www.google.com/amp/s/amp.cnn.com/cnn/2018/08/17/us/m...