Joe,
Whilst Europe may seem to be one homogeneous blob its not quite as simple as that....
Certainly in the Uk there is not need to have private health insurance at all, no matter how much you earn.
The reason to have private health insurance is mainly to increase the ease of access to and choice of medical treatment you get.
Going private does not equate to getting better medical treatment, in many cases private hospitals are far less well equiped to handle the unexpected.
Also note that ALL Emergency treatment is 'public', there are no private Emergency rooms, no private emergency ambulances.
So if you have private health car and you are in an accidnet, say your drive your Enzo into a lamp post the same ambulance crew will pick you up and take you to the same Accident and EMergency Department as the guys who drive is sh#tmobile into the lamp post. The same nurses will deal with you, the same doctors....and you will get the same treatment...in qulaity and quantity.
After that the private health care may make a difference in terms of 'hotel services' in a public hospital (private room etc) but the medical treatment will be the same, provided by the same staff.
Private medicine is a great help in elective complaints and in gaining access to medical care and chosing who provides it.. but it does not equate to better medical care.
Also ALL medics are trained in the same way, they all need to follow the same academic and clinical training, which is based in the public hospitals, not private, and are examined to the same standard. So the quality of the staff is not an issue.
A little aside is that there are very few private hospitals that have Intensive Care services avaliable, so all major surgery is undertaken without that back up and with the full knowledge and agreement that if something goes really really wrong you will end up in a public hospital being looked after by the required medical serivces who look after everyone...
The system here is so fundamentally different that comparisons are at best 'entertaining' but mainly irrelevant.