An MRI cost me about 0€.
A 4000€ test which tests for nearly any rheutmatic diseases markers and the visit to the hospital for that test cost me 0€, both things got done within two weeks.
Even if you are poor and want to go to a private doctor it will cost you not nearly as much as in the usa. For me it was about 100€, for one visit and that was on the higher end.
Socialized healthcare is always cheaper.
My mom is a doctor, she worked ICU, ER, etc, board certified in 10 states and holds a medical license in 3 countries(yes, she did residency three times, it's a long fascinating story for another time). Eventually she decided to open a private practice for family medicine bec it was less stress, but she's got tons of experience, and is highly regarded, and she charged less than $40 a visit for the uninsured. She would spend ages talking patients out of procedures that were harmful or simply unnecessary. You got high end care from her each time.
The gist of this is: you have no idea what you're talking about and individual anecdotes don't prove one system is better then another.
I'll just add as food for thought: nothing is free, avg effective tax rate in EU is 50%
Avg ETR in the US is less than 30%.
If there is demand for private healthcare affordable to the middle class, the demand will be met with supply.
And if that fails, they should be taught about democracy.
That if it turns out that socialised healthcare doesn't work for most Americans most of the time, then the country can revert to the system it currently has.