"Not sure what your point is here. We shouldn't test for STDs? People who enjoy having sex are evil?"
No, but some people definitely abuse with free testing every few months. I am not kidding here. Why do you or I pay for their frequent switching of partners without them being more cautious?
For the same reason you pay for people who don't exercise enough, eat too much, drive poorly, don't go for periodic preventative check-ups, smoke, drink alcohol or coke, ski, box, canoe, eat bacon, play football, hike, collect garbage, donate blood, work as a nurse, doctor, or other hospital worker, work in mines and other heavy industry....
In both the US and Canada, because it is essentially an insurance model, everyone pays for the negative decisions of everyone. The fact that some people like to have sex with different people get checked for STDs doesn't seem that different than me eating bacon and needing to get cholesterol checked occasionally.
Also the bigger issue to me is what that "abuse" costs, and it's a bit silly for us to argue about it without a good understanding of the costs. My SWAG would that there's about 10 million people between the ages of 20 and 40. Say 5% of those swap partners a lot, and of those, 10% go to the doctor quarterly to get tested at a cost of $100. Then the total cost would be $20M, which doesn't seem like that bad a deal. Isn't a heart attack from eating too much bacon running in the tens of thousands? You don't need many of those to exceed $20M. (I imagine AIDS is pretty expensive to treat too, though.)
"That said, I think that Canada actually has the best of both worlds--everyone gets good healthcare at reasonable prices, and rich, grass-is-greener people can jump down to the USA."
Here I disagree with hours in line, months to get some treatments. And do you think that Trudeau or Harper would wait at all? No. And they get the most competent physicians/specialists right away. So it is not fair for everyone.
They also pay for round-the-clock security for the Prime Minister, because we think it's a good idea to keep him not dead and functioning effectively. If you're going to suggest "not fair" examples, it would be much more persuasive if it weren't the leader of the entire country. (Like say, his wife and kids, who would also probably jump the queue. That would be an awesome political controversy.

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That said, my goal would never be total fairness. Naively striving for absolute fairness is pointless--we need to be practical, not live in fairy tales. My goal is to reduce the effects of luck in life, so the people who work the hardest have the best possible chance to get ahead.