You are wrong; in my opinion. The government is our employee; like a dog on leash there to serve us as we direct.
It is we the peoples job to care about our fellow man and citizens. We may or may not use the government to do that.
We have gotten SO USED to the government doing things they shouldn’t be doing; that we can't tell the difference anymore.
If my neighbor is having trouble taking care of his house; I shouldn't wait for the government to take of it. I should offer to go over myself and help him myself. Same thing in my area when they didn't clear the snow off my bike paths. I finally just went and cleared it my self.
The way I read scripture, I see a mandate for government, the church, and individuals to care for the poor. That the mandate exists for individuals does not negate the mandate for the other two.
There are very specific instructions to kings and their rule is tied to it. I posted one of them.