In return for "paying for someone elses health" everyone else pays for yours as well. How would you feel if you suddenly came down with an illness and didn't have thousands of dollars to pay out of your own pocket. Then you'd be wishing for others to pay for your health. With a cycle, there is equilibrium.
America should have free universal healthcare like France, England, Canada, and Cuba. There is really no downside to universal healthcare besides having to increase our taxes. But think about it, yes you have to pay a little bit more to buy things or pay bills, but it's not one big, all of a sudden lump sum. Not everyone can just dig around under their couch cushions and find 10,000 dollars to have a baby, or to treat their Cancer. And they shouldn't have to. All the places in the world that have universal healthcare are doing just fine, they have a lower infant mortality rate and outlive us Americans.