This is such an American take.
If you're unhappy with the wait time then get private insurance and go to a private doctor, just like you would in the US. But if you're too poor for that, at least you get something in six to twelve months instead of nothing or bankruptcy. And your insurance will be much much less because you're getting most of what you need publicly. Your US insurance is in the order of three to five times as much as private insurance in the EU, so your taxes are lower, but your costs are too.
The real problem always seems to be that universal health care would leave rich Americans worse off (higher taxes), would likely be about a wash for most middle earners (higher taxes, but none/less health care costs), but would leave the poor significantly better off (who are totally stiffed in the US at the moment).
So, by saying you don't want universal health care you're effectively saying that you're rich enough that you don't care about it, and you don't want poor people to be able to get health care at all, and if some die early or go bankrupt at least it isn't your problem.