If something is free depends on the country.
And obviously tax paid is not free for the society.
For example: in Norway and Denmark (I think all Scandinavian countries) employers and employees do not pay into health insurance. The "portion dedicated to health care" It is included in income/labour taxes.
In Germany (simplified) we have mandatory health insurance. Which is paid 50 - 50 by the employer and the employee. It used to cover the whole family of a single worker ... no idea how that is right now.
While in Scandinavia a doctor visit is completely cost free, in Germany you have to pay a token fee (which can be extremely high). In Scandinavia typical medication is free. In Germany you get it from a Pharmacy, and pay a token fee again.
In Germany hospitals try to keep a patient a day longer than necessary, or two. To "get income". In Scandinavia they get kicked out as early as possible: because they want to save costs.
Universities are more complex. But standard schooling is cost free. Of course we have private schools ... and people use them for what ever reason.
My studies were cost free for the first 5 years, then I had to pay. Has I taken the PhD offer, I would have been paid for my further studies.
Luxembourg has free public transport. Even for foreigners.
Germany has not a German wide ticket for public transport that costs $30 for low income people and up to $65 for normal income, per month.
Nearly everywhere in Europe you get extra aid for kids. Which can be significantly high. For example, first child about $300 per month, up to $600 for 3rd and any further child.
If housing is affordable, depends on the country and rules. It is cheap in Portugal, Greece or rural Spain, France or even Germany. And absurd expensive in London, Paris or Duesseldorf. Germanies capital Berlin is surprisingly cheap.
What I want to say is: free is paid with taxes. Taxes are based on income. So low income people seriously have everything relevant: healthcare, dental care, school for the kids and other benefits: for free. The richer people pay higher taxes, but obviously have on paper all the benefits for free, too.
Schoolbooks still cost money, but often are traded down from higher grades to lowers. And in special cases the state supports buying school books.
People like to emigrate to USA because they hate the rules in Europe ... to much paper work. Or think it is easier to get rich elsewhere.
However counter examples are companies like BioNTech ... to Turkish scientists from an ethnic minourity, migrated to Germany to found their research company ... and in the end, Pfitzer made them rich.