>>512693702The issue with a two-tiered system is that encouraging the wealthy to access better healthcare for prices the rest of us can't afford means the rich are entitled to be healthier and live longer because they're rich. Since the private system would still need to be publicly regulated, it would siphon public funds away from public healthcare to ensure the compliance of private clinics which can make enough money off of rich clients to make legal noncompliance profitable.
You also run the risk of well-funded private lobby groups who access the private system pressuring the government to erode public services to redirect funds towards the parallel for-profit system, or the public sector being priced out of emerging treatments and innovations because they're outbid by their own private sector, creating not just a duplication of administrative burden but of technical, scientific and entrepreneurial efforts.
The latter is exactly what happened in Quebec. It has public healthcare now in name only, because it bit the bullet and tried the two-tiered system, and the wealthy donors to provincial MPs immediately lobbied to erode public services to almost nothing in favour of the private ones they could monopolize, creating a deeply corrupt and nepotistic system in which the oligarchy and their friends make all the money while the taxpayer pays for healthcare they can't access. In practice it takes the authority for a key public service which is distributed among many accountable bodies and concentrates it within a single decisionmaking entity with direct financial incentives to fuck everyone over.