Australian system seems alright to me in Australia, and I'm from the UK. A mix of free and private.

The 'free' service costs increase every year over 30, that is taxed from your income on a % basis if you do not pay for a Private Health Insurance. If you do not earn a lot, you do not pay a lot for the taxed healthcare, if you earn a reasonable amount, by paying for a basic Private Health Insurance cover, the free service care costs do not increase, which could cost a lot after a few years of % increase.

If you pay for private, you can still use the free service, but expect longer queues and waiting times, and you also have limits on what services you are entitled for free. If you use private, you have to pay to see the Dr, but you'll most likely end up with a rebate covering much of the costs.

It isn't perfect, but I prefer it to medical facitilies in the UK.