It's not meant to "encourage the rich to support" the health system, it's meant to avoid completely gutting the public health system by creating a parallel pay-for-play system where only the richest pay and subsequently suck up all of the already finite resources and talent.

Introducing parallel private health care is just accelerationism for privatization wonks who want to just see the death of universal healthcare by sucking it dry for those willing to pay.

There's no magic wand with the resources available for healthcare. Creating private systems so rich people can skip the line doesnt magically create that capability, it means taking that capability from someone who maybe needed it more in the public side of things.