Nominal rates might be, but tax burden is not. California tax burden is well under 15% GDP, and federal collections in the state are a tiny bit higher than state tax revenues, together still under 30% tax burden. EU overall tax burden is over 40% of GDP.
Then you are counting the cost of the thing you are complaining about not getting for your supposedly-equivalent taxes in order to try to justify the claim that the taxes are equal.
Perhaps the european model is better overall, or perhaps there are other complications. Regardless, the debate is not "free" vs "pay private companies". Both models have costs and benefits.
Also, consider that EU tax collection is comparable (and often lower) than US tax collection, despite not EU not having to separately pay for education and health...
No one in Europe is under the illusion that public services are free. This is a complete strawman. But they are much more cost-effective than the alternative, a lot of the time, and provide universal services to everyone and help maintain the social fabric of a society.