To increase supply in this case, new hospitals, doctors, medicine etc all need to be increased which would increase costs, population increases would increase demand, so prices would still increase I think if we took the time to chart everything out, i am not sure the healthcare market works like the basic supply and demand setup.
I think it would look more like this:
The Quantity is increasing (along x axis in (b), As the Supply increases, but the shifts in Demand also cause prices to increase, but then settle back down in the long run. This is why it is so much of a pain in the butt to explain for someone like Bernie on the campaign trail. Populist messaging sells, reality bores people.