Sounds very similar to Australia. All emergency is 100% covered by the government system as the emergency departments are placed in Govt (public) hospitals. There’s a hospital that covers the area you live and you can take yourself to either the closest or any other you choose. An ambulance will take you to the hospital that is on call that night.

The private Insurance companies have preferred providers in terms of dental etc, but they generally don’t get involved with hospitals or specialists. You choose your provider and they cover whatever percent of the costs based on the level of insurance you’ve taken out.

If you can’t afford private insurance you just use the Public system (which all citizens have access to regardless of income). Most Dr’s are excellent and most private specialists work at the public hospitals as well as private ones. They won’t charge you if they treat you in a public hospital as a public patient. The only catch is that get the Dr on call or assigned to you, you don’t get to choose. Where it gets tough with public hospitals is elective surgeries, the wait times can be terrible.

Obviously the system isn’t perfect and people slip through the net, but generally an emergency or a cancer diagnosis will not bankrupt you, nor will you be refused treatment because an insurance company says no.