European countries do have more doctors per capita, which is good.
They don't have nearly as much resources in the system, though. Come to a doctor with a bad cough, get a prescription for Paracetamol. You got to have a pretty bad infection to get a prescription for an antibiotic. Endure a long discussion with a doctor to renew an antidepressant prescription made in another country.
Lines are pretty long, too. Wait for two weeks to get an appointment about your coughing and sneezing. Have a deteriorating chronic condition and be prescribed painkillers and be told to wait for a year. You're not yet feeling so bad as the people who are currently being treated and who take up the capacity; these people also waited a long time.
All are examples from my friends dealing with the health systems of Netherlands, Sweden, Germany.
The US system has a ton of issues, but I still take it over these European systems. Have I been floored by medical bills? Yes, from my dentist, from my wife's heart surgery. But I somehow managed — and we both received instant, high-quality help.
Even the Russian system is better, or used to be back in the day. You could buy local insurance, and the choice was reasonably wide. You could pay upfront in cash, and the sums were manageable — Moscow definitely not being a cheap city, more expensive than many EU capitals.
Of course, I'm talking from a perspective of a well-earning software engineer who lives in metropolises, not in countryside. Still I think that either system has downsides, and the European systems are not superior, but just suck differently.