single payer would be similar to the public school system.
The tax for it replaces the cost of private schooling, if private schooling were all that is available, the premiums are more than the tax, that is the point. There is no 'increased cost'.
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Brits are a gov run hospital system.
Canadian are non profit clinics operating under the gov.
Both of them spend less per capita than we do in America.
AMerica medicare is for profit clinics (including non profits) paid for by 'single payer' idea.
I have medicare and I do not wait very long at all, nor have I ever been neglected. The clinics I use compete in a market place, of which I can choose my doctor and clinic.
Moreover, Canada and Britain are much more stingier with their health care dollars than America is.
Moreover, the issue is much more complicated and deeper than you are making it out to be.
one thing is certain, comparing Canada and Britain to an American style 'single payer' medicare for all idea is not an apples to apples comparison.
But, even in Canada, not everyone agrees with your premise: