You framed Luxembourg as a ‘beautiful’ place and to that extent, yes, it is because of their socialist-democratic policies.
But okay, if we go along with your view—say you’re right and I’m dumb—then that must be the reason why the strongest capitalist countries with a good quality of life in the world have strong socialist-democratic and welfare-state policies, right? Also the reason why capitalist Somalia, capitalist Haiti, capitalist DR of the Congo, capitalist Afghanistan, and capitalist Mozambique—countries with nonexistent social welfare—have it so bad. And the list can go on and on…