Why don’t we have two-tiered healthcare in this country?

We can still have a public system based on need and the principles of triaged care, but if there are wealthy people willing to pay for premium care and to cut the line, why don't we let them instead of flying to the US to do that? Couldn't we better use that money here, for our economy? Having a private system, alongside the public one, would take pressure off the public one, greatly reducing wait times and making things more streamlined.

The current system of public healthcare is collapsing and doesn't appear workable. Something has to give. Something has to change.