Like most physicians, Dr. Ben Carson has a funny story about the behavior of insurance companies.

He once had a patient for whom he was recommending a hemispherectomy, a rare procedure that calls for removing half the brain. The patient’s insurance company refused to pay, calling the treatment experimental.

But Carson — a graduate of Yale University and the University of Michigan Medical School — persisted, and, after much wrangling, the insurance company relented. However, the company stipulated, if this particular patient needed a second such procedure, it definitely wouldn’t be covered.

“It gives you some idea what we deal with. Guess they didn’t want anybody to be like them,” Carson joked during a Nov. 23 meeting with the Las Vegas (Nevada) Review-Journal editorial board.

In a more serious vein, however, Carson called insurance companies out for what really ails them: “Insurance companies are notoriously interested in themselves,” he said. And that’s absolutely true. Insurance as a business thrives when companies take your premiums, invest the money and distribute that cash to shareholders. It suffers when it actually has to pay for things, which means your interests as a patient and their interests as a company diverge at the very moment you need them most.

Don’t believe it? Look at the recent announcement by insurance giant UnitedHealth Group that it may not participate in health insurance exchanges under the Affordable Care Act after 2017. One of the reasons? People who sign up for insurance on the exchanges actually use their policies! The horror.

But don’t mistake Carson for, say, fellow presidential candidate Sen. Bernie Sanders, I-Vt. Sanders quite reasonably says the insurance company model is fatally flawed and recommends a single-payer, Medicare-for-all system, the likes of which we see in other industrialized nations.

Carson agrees with the diagnosis, for sure. “I think we need a better system,” he said. “The current system is abominable. People’s premiums are skyrocketing. A lot of people are not seeking care because the deductible is so large, and that’s impacting upon their health. So no, it’s not a good system that we have now.”

But Carson’s cure is much different than Sanders’ idea. Carson supports the near-universal use of health savings accounts (established at birth), where money can be deposited to cover most medical problems. Money could be transferred among family members and inherited by kids from parents when they die.

The only real place for insurance in Carson’s scheme comes in the form of catastrophic coverage, prices for which he says will be far cheaper, since it would be used only in the event of rare emergencies. (Today, an emergency like that can bankrupt a person or a family.)

“We ought to put the decision-making process into the hands of the patients and the health-care providers,” Carson said. “That is absolutely critical. And when you do that, it actually helps to solve a lot of problems, because it will bring the whole health-care system into the free-market economy, and that’s what will control pricing and quality.”

There are still problems with Carson’s approach — especially when it comes to indigent people — that wouldn’t arise in a single-payer system. (Carson said current Medicaid spending is sufficient to buy all participants membership in concierge medical practices, if the total pot of money was divided among the plan’s participants.) But under his plan, we’d still be dealing with a business model that profits from treating human illness, which is not a good idea.

But it’s telling that Carson’s vision for reform represents such a radical, and not incremental, change. If we could start from scratch, we’d never design the system of health-care delivery that we have today. On that, we can all agree.