Tyro lets slip the real liberal agenda:
If someone was advocating for something because "Europe does it," they'd end up advocating for some hybrid model of public and private to ensure universal coverage. Your explanation does explain why generally liberals aren't advocating for an NHS-like system, since liberals aren't big Anglophiles. However, since we're all closet communists, what we actually want is for an iron-rice-bowl system of guaranteed jobs in nationalized state sector industries followed by patriotic worker songs sung in unison at the end of each work day.
Ssshhh!