It's gotta be both. A fully public system can't meet the health needs (and wants) of everyone. So those who can afford it should be able to get their health care outside the public system. That way the public system can serve those who need to use it better. But even those who generally use the private system still have access to public health care, esp when it comes to emergency services.
Besides you can't restrict people's freedom of choice. And that includes doctors who want to work outside of the public system.
We've always had a mix of private and public, and by and large it works OK. It also keeps insurance premiums low, because insurance companies have to make private insurance attractive enough for people to pay for what they can get through their tax dollars (albeit sometimes the care they need comes a slower than in the private system).
“The fundamental cause of the trouble is that in the modern world the stupid are cocksure while the intelligent are full of doubt.” - Bertrand Russell
"When the power of love overcomes the love of power, the world will know peace."
Jimi Hendrix
