One does not have anything to do with the other. Elsewhere on the planet, the government pays the bills, the doctors keep the records.

In Belgium's case, payments are handled by an intermediary of the patient's choosing. Those organisations see a fair amount of detail but that is as far as it goes. The government only sees coded diagnosis data (coupled to length of stay if a hospital is involved.)

There is a push going on to towards digital records, but those still reside at the doctors offices. Hospitals do manage all the data for their specialists.

AFAIK, the Brits are the only ones pushing for a central medical database as you describe and it is not going very well.

Besides, what do you see the government do worse with your medical data than a profit motivated insurer already does today?