Not necessarily the closest a major democracy has come to Libertarianism that I can think of would be America in the 1870's-1890's which unless you were very wealthy was a completely horsehockey place to be. Similar situations were in Europe, and that's why Communism developed.
On the flip side, command economies haven't been much fun to experience either, so to postulate that only one of the two systems has some problems 'alleviated' is indeed to skew the choices.