Europe is far from perfect though. In all the three countries I'm familiar with (UK, Sweden, Spain) the healthcare system is really struggling. Extremely long wait times are becoming more common, for more procedures, even in the emergency departments.
But the taxes remain very high, especially on income so it hits middle-class professionals the hardest. In some countries like Spain (and increasingly Sweden) they are contributing to a high structural unemployment, especially youth unemployment, too.
So in the end, the problem isn't just higher taxes, but higher unemployment and therefore lower gross salaries (before those higher taxes are even taken into account).
Long wait times are increasingly also a major problem in US healthcare, so I'm inclined to believe that the root causes behind wait time problems aren't related to public vs private insurance systems.
I wholeheartedly agree with that sentiment. We are definitely heading in the wrong direction. It's the same development here (not UK, Sweden or Spain)
I'm paying maximum social security and in previous generations the service you got in the public healthcare system was way better.
For some procedures I definitely go to private doctors as well nowadays. It's not a huge burden, but e.g. I will never go to a public skin doctor ever. The stories you hear about them are... brrr!
But overall the system is still miles ahead of the one in the United States. I've been there on multiple occasions and witnessed first hand, I have friends there and I know both systems. (Obviously I know the European system or rather the one in my country of residence even better)