Or let it become a market again, like it was for our parents until these subsidies came along.
Letting healthcare become a truly free market literally means having people die on the streets from preventable diseases if they can't afford to treat them.
Most civilized nations have decided that they don't want that kind of thing a long time ago.
For this to actually work, you need to either regulate prices, or have a public-owned, government-run nonprofit with an explicit mandate to keep the prices as low as they can be, regardless of demand - and throw subsidies only at it.