First off, most people don’t need heart-lung transplants, so you’re arguing from an edge case. Second, a good health insurance plan, if bought into early, will take care of that. Third, GoFundMe and social media campaigns exist and are successful, not to mention charitable groups like Catholic Charities, St Jude’s, etc.
None of these have a 100% chance of success, of course. But single-payer will cause more cases of failure than the government getting out of the health care business in general.