At the end of the children’s nursery rhyme, “all the king’s horses and all the king’s men, couldn’t put Humpty Dumpty together again.”

That’s the lesson Americans should bear in mind as we witness the implosion of ObamaCare — sometimes, once something is broken, no amount of effort can fix it.

President Obama has now admitted his promise that “if you like your health-care plan, you’ll be able to keep your health-care plan, period” — a promise he made at least 23 times — ended up “not being accurate.”

But this was not another “glitch” in the ObamaCare rollout, like healthcare.gov. It was a key feature of the law. ObamaCare is built around the idea of forcing the young and healthy to overpay for insurance in order to subsidize the old and sick. That is the reason why the law includes the infamous individual mandate, requiring all Americans to have insurance.

If the government is going to require you to buy insurance, it must define what is and is not insurance. To satisfy the mandate, insurance has to meet certain government-defined standards. This is only logical. If young and healthy people could buy less-comprehensive plans than the older and sicker people, it would defeat the whole purpose of the mandate.

As of this week roughly 4.8 million individual insurance plans have been cancelled because they didn’t meet ObamaCare’s exacting standards, such as providing as maternity care (even if you were a man), alcohol rehabilitation or contraceptives. Another 5 million are expected to lose their coverage.

Few ObamaCare supporters truly mourned these cancellations. After all, they believed that those plans were, in the president’s words “subpar.” The people who bought these plans just didn’t know what was good for them.

The people, however, disagreed.

In response to the public outcry, Obama offered a temporary “fix.” People with noncompliant plans will be able top keep their policies for one more year, but only if insurance companies choose to do so, and state insurance commissioners go along. And while insurers could renew existing plans, even if they don’t meet ObamaCare requirements, they still cannot sell those policies to anyone new.

The problem is that insurance plans are not simply a list of benefits on a piece of paper. They are a complex interrelationship of benefits, the pool of insured customers, a network of providers, and so on. And, because for three years insurers have been told that they could not sell noncompliant plans, many of those plans simply don’t exist anymore.

Even if they could be recreated, which is doubtful, it would be a time-consuming and costly process. Moreover, many of those who have had their plans cancelled have already bought new policies, sometimes with different insurers.

As Robert Laszewski, of Health Policy and Strategy Associates, points out, purely as a practical matter, “[T]his means that the insurance companies have 32 days to reprogram their computer systems for policies, rates and eligibility, send notices to the policyholders and then enter those decisions back into their systems without creating massive billing, claim-payment and provider-eligibility-list mistakes.”

Moreover, since only some customers will return to their previous plans, and insurers are still prohibited from selling the plans to new customers, the pools for these plans will inevitably be much smaller, spreading the risk over fewer people, meaning that premiums would have to rise.

All of this is why state insurance officials are balking at implementing the president’s “fix.”

There will be a ripple effect throughout the insurance system. You simply cannot require insurance companies to cover people who are sick without raising premiums unless you can force healthy people into the system. But younger and healthier people are more likely to try to reclaim their previous, less expensive policies. Older and sicker consumers are more likely to forgo those plans and take advantage of the more comprehensive policies sold through state exchanges.

That undermines the entire premise of private insurance, leaving the pool of people in the exchange much sicker and more costly, driving up premiums and possibly causing the entire structure to collapse. Actuaries call this the “adverse selection” death spiral.

ObamaCare is broken beyond fixing, that much is clear. But it also seems like Obama has damaged the entire health-care insurance system in the process.

But for some Democrats, that’s not such a bad thing.

After all, if ObamaCare crashes and burns but takes down the private insurance system with it, we can quickly expect Democrats to push for a government-run, single-payer system. Indeed, some Democrats have seen that as the goal all along. Senate Majority Leader Harry Reid has said that he sees ObamaCare as just a step on the road to single-payer.

One should never assume conspiracy when simple incompetence will suffice. But whether by accident or design, the failure of ObamaCare may be opening the door to even greater government control of our health-care system.

This article appeared in New York Post (Online) on November 17, 2013.