You're argument is bullshit and comes from a place of ignoranceYou need to learn to argue civilly. Then you might not get down-voted.
No, the province of Quebec did...
Fine, that doesn't affect my argument.
You just gave examples in both Canada and the UK that showed that you most certainly can.
No. There's a difference. The UK system says "we'll give you $X for treatment A; if you want the more-expensive ($Y) B you get 0". What I'm arguing is "we're willing to invest $X; if you want B, you'll have to kick in Y-X".
In concrete terms, suppose that my hypothetical colon cancer can be treated for $50,000 but there's also a $60,000 treatment that's better but the government doesn't cover. The UK says that I have to "take it or leave it"; they won't let me get the alternative by kicking in the extra $10,000. I'd have to pay the full $60,000. For practical purposes, that's all but a prohibition.
You're fighting each other for a dwindling and ever more expensive piece of the pie
This is wrong. The pie is enlarging; everyone has access to better healthcare than anyone could get 60-70 years ago. The increasing expense is due to the availability of additional treatments. As Mr. Kamen said, there are treatments (e.g., polio) that were in effect infinitely expensive two generations ago that are now within the reach of literally everyone. The stuff that's outrageously expensive will be available for our kids.
But not if nobody develops them. If those researching new treatments can't sell those treatments because the gov't puts a wet blanket on the industry, then the treatments will never be sought.
Another thread in this page claimed that government funding would prevent this. There's a little truth in that, but it all revolves around the politicization of disease. We can already see the effects of that: government subsidizes AIDS/HIV research at something like 10x the rate of breast cancer, normalized to the number of people suffering from each. It winds that we help those with the best lobbyists, not those with the most need. And that's certainly no better than the Adam Smith's invisible hand could do.