Altogether, the average American’s health care costs more than $9,200 every year, though not even Bernie Sanders, who recommends a single-payer health care system, suggests the government ought to pick up the entire bill.

Now Mr. Carson is saying that the government wouldn’t necessarily fund the health spending accounts for everyone. “That is off the table,” he told Mr. Wallace. “We’re not having the government do that. I don’t want a big government program.” But he also said that people with Medicare or Medicaid coverage could get the money currently being spent for them in their account. What, if anything, he would offer people currently covered through the Obamacare coverage expansions is unclear.

What would happen to Medicare and Medicaid: Mr. Carson says that once people see the advantages of the health savings accounts, they will freely choose them instead of the 1960s social insurance programs for the poor, elderly and disabled. He says that he wouldn’t abolish the government programs, but that Americans would voluntarily give them up in favor of the health spending accounts.

As is the case with most insurance programs, there’s a wide range of health spending among people in those programs. Medicare, for instance, includes some hale 65-year-olds with few medical needs, and some people with complex health problems near the end of their lives. Medicaid covers poor children and childless adults, many of whom have low medical costs, and people with disabilities or long-term care needs, whose care typically runs more than $10,000 a year.

In a system where people choose between cash or government insurance, healthier people will probably opt for the cash. But that preference is likely to change once they get sick and medical bills start piling up. This tendency of people to wait to join costlier programs until they get sick is a reason most government insurance programs provide financial incentives to get in early and stay in — so that risks and costs can be spread across a broad population. Medicare’s drug program, for instance, charges higher premiums to people who wait a few years to join. And Obamacare imposes fines on anyone who fails to obtain health insurance. Mr. Carson’s new plan, by contrast, appears to pay healthy Americans to stay out of the insurance pool.

His original plan solved this problem by eliminating the more generous insurance programs, so people would be forced to either save in their spending accounts or forgo care. The new plan runs the risk of costing the government more than the current system, since people could game a two-choice system, sticking with a savings account when their spending is low, and switching to a government program once their medical costs rise.