Let’s get the obvious out of the way: As chief executive officer of AOL Inc., Tim Armstrong shouldn’t have stood up and blamed proposed changes to the company's 401(k) plan on two discrete  and, to many AOLers, recognizable medical catastrophes. Armstrong’s specificity -- he blamed high medical costs stemming from two "distressed babies" of employees -- was unnecessary, cruel and dumb.

Although Armstrong’s comments were a disaster, the problem he’s facing is real.

Large companies such as AOL self-insure. Even companies that are much smaller than AOL self-insure. That means their risk pools are made up of their employees. If their employees are older or sicker than average, their premiums rise. If their employees have an especially bad year healthwise, costs can be shattering. So a company will look to offset increased expenses by cutting health benefits or staff, raising premiums, changing 401(k) plans, raising prices or some other fix. Self-insured companies often have a secondary form of catastrophic insurance to help blunt the effects of particularly bad years. AOL presumably has this, too, in which case those $1 million babies probably cost the company a lot less than $1 million. But over time, the costs do add up.

This is the real problem AOL faces: Among industry peers, it is an older company with a large, aging workforce. Its benefit costs look worse every year. That might be fine if the business fundamentals looked strong. But AOL’s profits rely on pricey dial-up service for customers who don’t know there are better, cheaper, faster options. The company’s core revenue driver -- accounting for more than $150 million in the last quarter -- is like a carton of milk that’s way past its expiration date; to everyone’s surprise, it still seems to smell fine, but it won’t for much longer.

So Armstrong has real problems. But in targeting AOL’s spending on health benefits, he’s identified the wrong culprit. The issue isn’t the families who had to watch their newborn children struggle for life in an intensive-care unit: Health insurance exists for exactly those families in exactly that situation.

The problem is the employer-based health-care system. It’s never made a bit of sense for health-care benefits to be routed through employers. The system emerged in the U.S. by accident. Wage controls during World War II made it impossible for companies to attract workers by offering higher salaries. Because health benefits were exempt from high wartime taxes, companies began using them to attract talent. After the war, unions joined employers in pressuring Congress to ensure employer-based health benefits were never taxed. So the U.S. emerged with an odd system in which a dollar of untaxed employer-based health benefits was worth much more to a worker than a dollar of taxed salary. Employers became the main vehicles for insurance not because anyone thought it was a good idea, but because the tax code made it a bargain.

The result has been a disaster for employers and workers alike. In Canada, the risk pool is effectively the entire country. Two costly pregnancies have barely any effect on aggregate costs. In Medicare, the risk pool is 49 million beneficiaries. A few patients with catastrophic health problems won’t budge those numbers much. But in our employer-based health-care system, the risk pool is often a few hundred, a few thousand or a few tens of thousands of employees. A bit of bad luck can be catastrophic.

The great mystery of U.S. health care is why the country’s CEOs didn’t demand a single-payer system a long time ago. It’s an unending distraction -- and cost drag -- for companies to employ expensive human-resources divisions to negotiate with insurers and hospitals, manage health-care costs, and field questions and concerns from employees. Companies that are great at making cars or buildings or accounting software can’t survive if they’re not also successful at managing health insurance.

The system persists for reasons that will be familiar to anyone watching the rollout of the Patient Protection and Affordable Care Act: Change is scary. No CEO wants to deal with the outcry from employees who are terrified that their benefits are being outsourced to the government. And few CEOs trust the federal government to manage benefits with any skill -- they worry they’ll just end up paying more in taxes than they do in premiums. That worry is often particularly acute for CEOs themselves, who would pay disproportionately in any system that relied on progressive taxation. Finally, their suspicions are typically reinforced by dire predictions from their HR managers, whose jobs depend on the survival of employer-based health benefits.

The result is that CEOs hate the current system but are too fearful to move to a different one. Consequently, they've made themselves -- and their companies -- vulnerable to “distressed babies.”

An irony of Armstrong’s predicament is that Obamacare, which he partly blames for his company’s increased costs, might be its salvation. Starting in 2017, states can choose to let large employers enter state health-care exchanges. That means companies would be able to add their employees to a much larger risk pool  -- in some cases, millions strong. Those companies would no longer have to worry about a bad year for employee health. Their insurers couldn’t ceaselessly jack up prices because expenses soared in one year, or because employees are getting older or sicker. If employers flock to the exchanges, it could -- finally -- be the end of our insane system in which each workplace is a tiny welfare state unto itself.

For that reason, the strangest thing about Armstrong’s comments wasn’t his frustration that his company can be so easily rocked by health-care costs -- it's his hostility to the best chance for relieving that burden.

(Ezra Klein is a Bloomberg View columnist.)

To contact the writer on this article: Ezra Klein in Washington at eklein22@bloomberg.net.

To contact the editor responsible for this article: Francis Wilkinson at fwilkinson1@bloomberg.net.