Money is fungible. Generally, the higher level of services is paid for by the higher level of overall taxation - you can call it fees or whatever, it doesn't change the fact that on average, you are left with less disposable income. This might be fine as a societal choice, but just don't think it's free.
It's no free, but it's shared on everybody in a way that we don't feel it's a burden, and everybody gets access to decent healthcare without having to worry about it.
"the higher level of services is paid for by the higher level of overall taxation"
Not necessarily. You can also try to reduce the cost of the service. Healthcare in most European countries costs less than in the US for the same service (for instance medical acts prices can be largely controlled by the state).
Honestly, I don't know much about economics. However I think it's fair to say that in that particular field, what may be great on paper may not work in practice. The theoretical models are so remote from real life that I'm not sure they provide much value. So it essentially boils down to ideology.
If one has to be dogmatic, I would privilege "free" healthcare and education to private property and free market.
