The sole fact that mostly capitalist countries provide healthcare for the unemployed is by no means a testament that capitalism is fundamentally compatible with this idea.

No country is purely capitalist or socialist - it's always a mix of the two. Sometimes it's a somewhat even balance, like in some European states. Other times one clearly dominates, like in the USA.

Universal healthcare is a concept deeply rooted in socialism. It functions within mostly capitalist countries, because they've decided to implement some socialist policies. Not because it follows capitalist thought. Because it doesn't.