I feel though, there are more successful examples of it working than there are examples a deregulated health care market working (which is what is advocated by many -- "why can't it be just like the cell phone market?" -- search for sibling posts around here to find it).

It isn't but in most countries that have single payer - you also have the option to go private if you can afford it. Single payer is there if you need it so no-one goes bankrupt, but those with the means can get quicker treatment if they want to pay for it.