> I constantly hear anecdotes about people waiting 6+ months for minor operations in the UK
Emphasis on the "minor operations". Things are prioritised by need and urgency, so naturally you end up with a long tail of non-urgent, minor operations.
> how the wealthy/elites of Canada fly into the US for treatments
There's a reasonable argument here that the US system has advantages for the wealthy. Generally however this is seen as undesirable.
> Everyone in the US already does have access to healthcare
There's several issues with this statement. The first is that 32.8 million people (12% of the population) were uninsured in 2019[1]. The second is that even if you have health insurance on paper, it's generally prohibitively expensive to use, only kicking in once a deductible is reached that will bankrupt you regardless (40% of Americans can't cover a surprise $400 expense [2] and these deductibles can run into several $1000). The reality for many is that if they're sick, they tough it out because going to a doctor may cause them financial ruin.
> above a certain income level you're expected to shop for your own. I much rather prefer that instead of it coming out of my paycheck in another mandatory tax without choice of provider.
I'm not sure what your experiences have been, but the only context where I've been able to "shop for my own" provider was when an employer happened to offer one of two providers in their available plans, which wasn't always. Functionally I had almost no choice in my health insurance coverage short of specifically finding a job that offered what I wanted, which given my priveliged position as a software engineer would be possible but would be laughable for most professions. Functionally, my health insurance was a mandatory tax without a choice of provider, it just wasn't a tax paid to the government.
I should also note that I now live in Australia, where we have a universal public system where I am still able to choose my doctor and other care providers. In fact, I feel that I have far more choice here than I ever did while living in the US.
[1] https://www.cdc.gov/nchs/fastats/health-insurance.htm
[2] https://www.cbsnews.com/news/nearly-40-of-americans-cant-cov...