Your story resonates with me, because on a number of occasions over the past couple of years we've taken my daughter to the ER.
Thankfully, in Australia, we have public hospitals so it doesn't cost a cent. Though I often walk out of there complaining that we had to wait 3,4,5+ hours.
Health insurance is a scam, and it puts upward pressure on the cost of health care to those that do not have health insurance.
Unfortunately, in Australia, after you earn a certain amount, you have to pay extra tax if you don't have health insurance, so you end up paying for it one way or another.
In Europe as well you pay for it with your taxes.The higher amount you earn,the higher your taxes (healthcare included) will be.Yet at the end of the day,you are way better off financially when it comes to healthcare.Why did your daughter needed ER?
Shes been a few times now, usually flu, gastro, etc