Since ZZZS has an absolute monopoly in the EU, it should be abolished and the introduction of sickness funds (Krankenkasse) for compulsory health insurance should be allowed, say on an industry-by-industry basis, as is the case for example in Germany.
Similarly, supplementary health insurance should be abolished; insurance companies selling supplementary health insurance could be restructured into sickness funds, for example.
All sickness funds are private.
These health insurance companies would receive monthly invoices from contracted health care institutions and private doctors, which they would have to settle within 30 days. Of course, this requires a price list of all health services signed by all participants.