What you described is just welfare, not socialism. Socialism is collective ownership of the means of production, meaning there would be no need to re-distribute wealth as it would be fairly distributed from the start.
What you’re thinking of is more along the lines of what Scandinavian countries have, which is just capitalism with social democracy and extensive welfare programs.
I’ve noticed a trend in some new American media coming out of more openly positive depictions of socialism/communism. The new HBO The Last Of Us series for example has this scene, and the new Fallout series has a more centrist/neoliberal take but at least calls out how the right uses communist as a “dirty word,” though she qualifies the statement by first saying “I’m not a communist.”