You already pick up that tab. People without insurance go to emergency rooms and medical clinics. They get treated and don't pay. Medicare and VA reimburse the hospitals for most of this "uncompensated coverage" (or "uncompensated care"); and most states have a fund that pays out to hospitals which provide a certain percentage of uncompensated coverage.
And of course if those payments are insufficient, doctors and hospitals just raise their rates, which is then passed onto insurance companies, which raise their premiums, which you pay.