Elective surgeries aren’t unnecessary and delaying them is unnecessary pains and suffering and accelerate death. People don’t just decide to get new hips or cancer treatments for the fun of it. What does happen in systems like that is that people that are older get put on long wait lists, if you’re too sick a panel of bureaucrats decides to end your care effectively the government choosing to kill you to save money and given there is no other option, you can’t do anything about it. Not sure why people would consider that better or more humane.
As far as the other argument, private systems have a thing called insurance, I don’t have to worry about paying my doctors if I need a surgery, out of pocket limits are reasonable (so I can’t go bankrupt) and if in an accident I likely don’t have to worry about that, my insurance provider will happily sue on my behalf and get their share of the money out of the other party, in most cases insurance companies will settle these matters out of court though.
Given car insurance is unregulated, it is very cheap. Likewise dental and eye care is unregulated and very cheap, even less than the co-pay you pay for your government dentist and we go to the dentist twice a year, where I came from in the EU, we went every other year unless you paid privately.
Health insurance on the other hand is highly regulated, monopolized by the government by region and with ObamaCare became in some cases 3x more expensive. Still, even in the most expensive states like New York and California, people in the US pay less in taxes and private insurance than they would for government funded schemes although there are, as pointed out, ObamaCare, Medicare and Medicaid which are the government funded schemes, they do give the same coverage as privately funded insurance, no wait times, no death panels, but with higher deductibles, higher co-pays and they pay providers only 70% of actual incurred cost.