one reason why i left the US for my baby's care and delivery. I am a Hong Kong Citizen and I am entitled to public healthcare which basically means i pay next to nothing for any inpatient or outpatient care. and yes, it's similar to NHS, but we do have options (private healthcare) for those who can afford to pay more to get faster services.
for all my prenatal visits and the delivery of my baby, it's absolutely free including any blood work, any ultrasounds, but i do not get my own ob or midwife, so i get whoever is on duty that day (of course, i am welcome to get my own from the private healthcare providers, just have to pay for it, and still much cheaper than the US)
if i were to go see a doctor about the flu, i can either go to the public hospital, and the wait is probably about 2 hours and up and only pay US$10 for the visit and the meds. but i also have the option of going to the private doctor and be seen pretty quickly and pay US$30-40 for the visit and the meds.
sorry OP, i do not have anything to add to your question coz I wonder that myself.