There's a causal arrow in the other direction, IMHO: People like to believe in the 'law of the jungle' mentality and thus vote to cut the safety net. IME it's especially wealthy people for whom it's a kind of game, not trauma, deprivation (of education, health care, food, housing, safety) and survival, and who also get to pay lower taxes, Didn't Jamie Dimon talk about how he liked how 'animal spirits' have been awakened?
There is a safety net. Here's how I'd describe the situation:
There will be a number of people, fewer than the total who benefit from the safety net, who almost everyone would say it was good that they were helped.
There will be a number of people, fewer than the total who benefit from the safety net, who almost everyone would say it was not good that they were helped.
Most of politics around this topic is people's differing beliefs in the proportions of the above, and how bought in they are to minimising the latter count because they pay taxes.
I'm sorry, what? Only in the US helping someone can be sold as a bad thing. It's better to help a few more people that may not really need it than help a few fewer that actually did.
I think it's worth reading the complete comment and you'll see where what you said fits my wider point.
Instead of cooperation under a system with a social safety net, we get a game theoretic weighting on defection without a social safety net.