Lack of doctors? Due to low pay? While there is a lack of family doctors, whether it's due to low pay is debatable. Often times it's due to dissatisfaction with the government system that doctors will start a private practice.
Wait times have definitely gone down and the whole process is being streamlined through modern information technology. I'm not sure what perspective you can have though since judging by the fact that your friend had to have his parents take care of his surgery, you must be pretty young. In any case, waiting times for non critical conditions are long, true. However I'd rather have wait times dictated by a patients condition than by his wealth.
Wait times for non critical surgeries are an issue. It's a compromise for not having to worry about going bankrupt to get treated for something that could degenerate into a life threatening condition. If your parents are rich enough to drive you to the US and pay for non-critical surgery, sure I could see the wait times as being an inexcusable inconvenience. The difference is that you have alternatives available to you, whereas in the states there is no option that won't cost an arm and a leg.
High taxes aren't only due to healthcare. Even so, studies show that private healthcare in the states is more expensive than public healthcare in other countries. The only difference is in public healthcare your money gets wasted on government inefficiency (which can be improved in the long term) while in private health care you're wasting money on lining the pockets of insurance companies (which can't be improved over time, because they are inherently profit driven).
How is this due to the nature of public healthcare? Private hospitals can do the same under shitty administrators, the only difference is they're not as accountable and susceptible to public scrutiny.
Did you mean patients that die? Due to lack of staff? This will happen in any hospital. Private hospitals don't magically have more surgeons on call.
Your poor friend. Must be terrible being wealthy enough to seek alternatives to treatment when inconvenienced by long waiting times.
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In conclusion, you grew up privileged and have no perspective on what it means to be afraid to seek treatment because it might bankrupt you.