I find it fascinating that something as basic as health care can be so very different across the world.
We are so lucky in Australia to have a great healthcare system with our "Medicare". Basically general medical is free*
I can go to a medical clinic and see a qualified doctor (not of my choice) & not pay a cent. The government covers the cost of the consultation (which is around $55). I choose to go to my preferred health care provider, she charges me around $90 per visit, but then Medicare gives me back the $55 consultation fee so I'm only out of pocket the difference. If I need to get blood tests done then that's all included in the cost.
If my doctor (either my preferred or from a clinic) sends me for an x-ray then I have to pay for it, unless it is a service provided by that clinic.
Medicare also provides an annual optical check, but it doesn't cover glasses / lenses etc, nor does it cover dental. Specialists are not generally covered by Medicare, some will "bulk bill", but there's often a long waiting list to see them. Medicare does have allowances for special treatments, particularly mental health programs.
If I fell off a ladder & broke my hip & got taken to hospital, then everything that happens to me in that hospital as part of my treatment is covered. Drs, nurses, food, medication, x-rays, surgery, anaesthetic etc. I would be in a shared ward, and get the doctor that the hospital assigns to me.
The only thing I have to pay is for the ambulance.
Medicare doesn't cover elective surgery, and the waiting lists for non-urgent surgeries are ridiculously long. My mum (who doesn't have private cover) has been on a waiting list for 18 months for a basic cataract operation.
Then there's additional private health cover, and if I choose to have private cover, then the levy I pay on my taxes for health cover is reduced. With private cover I can choose to have basics only (ambulance, private hospital, doctor of choice), or add extras as required (everything from basic optical, through to obstetrics to prosthetic limbs). Because I can have my doctor of choice I also generally don't have the issue of sitting on a waiting list for non-urgent surgery.
Personally I have private cover with basic add-ons (dental, optical, physiotherapy) but will probably have a look at my options in the next 5 years or so as I get older. I've only had to use the 'general' part of it twice, once for an out-patient procedure at a private practice - I paid the $500 excess for what would have cost me nearly $3000 otherwise, and the other for an ambulance fee. I could have had the procedure done under Medicare, but I would have been waiting at least 3 months for it.
It costs me about $150 a month, probably a lot more than the difference in the tax levy I pay, but for me it's peace of mind. Plus I have shocking eye-sight, so I get my medicare-covered annual checkup, and my private covers my glasses (generally a new lens prescription every two years), plus my additional ophthalmologist tests & costs.
*Free being on the understanding that it's actually paid for by my taxes