The basic answer is that the progressive European countries primarily funded through VAT are indeed using a regressive taxation system, but countering it with progressive spending.

The US system is a moderately progressive tax system but less progressive spending (not no progressive spending, but not nearly as much).

The argument is that you "buy off" the wealthy interests (both wealthy individuals and corporations) by using a regressive tax system, so they are happier to let you spend the money progressively, while in the US they are constantly fighting any progressive spending, because any tax cut will benefit them greatly.