I don't know about Canada, but here in Spain you have both. You have public health guaranteed, but many people also have different levels of private coverages, usually to get quicker appointments.

As I understand Medicaid, it would just be open Medicaid for 100% of the US population regardless of the income, remove Medicare (they are now under Medicaid), leave the private sector as it is. Do you think Medicaid is too slow, too low quality, too terrible in general? Pay for private insurance, but you can still go to Medicare if needed.