It always intrigued me that the U.S., often five or more years ahead of us Europeans on so many issues, can't manage to have a basic healthcare system.
Not that I'm very knowledgeable on the subject, but everywhere in western Europe you would more or less have the following:
- each and every individual is covered by social security, which includes coverage of between 90% and 99.9999% (depending on the issue) of medical costs. Paid by mandatory social security contributions of employers and employees, and the rest is paid out of tax moneys;
- hospitals and doctors can decide that they want to be totally independent (in which case they can ask whatever they want as fees, but their clients will not be covered by social security) - quite obviously nearly no hospitals or doctors ever do this (those doctors would probably rather emigrate to the U.S. - there could be some brain drain here, but at the same time Belgian university hospitals have quite good ratings in terms of breakthrough findings, so it's not like we're lagging so much behind the U.S.);
- if a hospital or doctor accepts social security refunding of its patients, each and every of their interventions has a fixed fee (negotiated yearly between the government and the Order of Medecine). Do hospitals/doctors therefore do unnecessary interventions, such as screening a 90-year old on STD's? For sure that sometimes happens, but statistics help in scrutinising and sanctioning hospitals/doctors who do so. Overall not a big problem, although everyone who has ever been in a hospital probably has an anecdote to tell in this respect.
- additional private insurance can buy you the right to have a hospital room for yourself (instead of having to share one with one other person). And here is the only exception to the 'fixed fee' principle (and 'brain drain' dilemma): doctors in a hospital working on patients which have their own room for themselves, are free to ask a 'supplementary fee' (which is often 100% or 150% of the fee reimbursed by social security). Over the last couple of years, there's been a big debate on that subject, as it obviously creates a "two-tier" quality of medecine which some would want to avoid, but on the other hand we also do want to limit brain drain, and, thirdly, if you want to pay more to get better quality, why not, say some...
Anyway: if AP2 tries to kill you and you end up in the emergency room of a Belgian hospital, no-one will be searching your pockets to find out whether you're insured

.
And more importantly: not only is literally everyone, including illegal immigrants, covered, but those types of healthcare systems are apparently at half of the costs of those of the U.S. systems, as the OP mentioned. That is truly the most intriguing part !