Here in backwater Europe we had no private medicine for a long time. The outcome was massive healthcare black market. Semi-official price list you've to pay to nurses/doctors/etc to „premium“ care.
On top of that, official medical staff wages were crap. People were forced either work for peanuts (IMO nurses and doctors jobs are damn hard and they have to be paid well), take money under table or... emigrate.
Now we have mixed system and it's definitely better than it was before. Doctors gets paid well. Elite doctors tend to work 2-3 days in private clinics and then 2-3 days in public hospitals so you can still get hold of them for free. Those who have an inch for premium services can pay local&legal, so local economy wins.