Yes, and it would be even more expensive in Germany. But in both countries the insurance covers normally 50% of it, wherever you go. If not all. (Other sickness are covered normally 80% if not entirely whatever insurance you have)
You pay nothing for ER, 10eur/day for the hospital and a few eur for medication - but nothing even in the range for 50% or 80%
dental is also covered to a large degree but if you want state of the art you have to pay the difference yourself - but you can also add a private insureance for that for 100 to 300eur/year to have everything covered.
you can still fall through if you can't pay the monthly fee - but emergencies are also free even if you don't pay.
private insurance can be expensive but should usally cover also everything.
I'm public insured in Germany and no, dental is not really covered, I had to pay my routine treatment last time at the praxis, and it was not cheap.
Do you know that if you don't have insurance (which is however mandatory in Germany) you get an actual bill for the medical services?
For the dentist: They often bill you for stuff that is covered but it lucrative to add something to the bill.
You do not need to pay extra for dental if you choose the most basic treatment. Most people like their dental work to look like their natural teeth which does not count as most basic. That is why you had to pay, but only the price difference to the basic treatment.
And, of course, the doc likes to sell you some extra treatment (say "professional tooth cleaning") which will make her/him some extra money.
Same for glasses. The most basic option is free. If you don't like the coke bottle bottoms then you will have to cover the difference yourself.
It’s not like you’re taking up a hospital bed. It’s a sew up and show you the door operation.