Indeed, as the economist (and former Reagan adviser) Bruce Bartlett points out, high U.S. private spending on health care, compared with spending in other advanced countries, just about wipes out any benefit we might receive from our relatively low tax burden. So where’s the gain from pushing seniors out of an admittedly expensive system, Medicare, into even more expensive private health insurance?

Wait, it gets worse. Not every 65- or 66-year-old denied Medicare would be able to get private coverage — in fact, many would find themselves uninsured. So what would these seniors do?

Well, as the health economists Austin Frakt and Aaron Carroll document, right now Americans in their early 60s without health insurance routinely delay needed care, only to become very expensive Medicare recipients once they reach 65. This pattern would be even stronger and more destructive if Medicare eligibility were delayed. As a result, Mr. Frakt and Mr. Carroll suggest, Medicare spending might actually go up, not down, under Mr. Lieberman’s proposal.

O.K., the obvious question: If Medicare is so much better than private insurance, why didn’t the Affordable Care Act simply extend Medicare to cover everyone? The answer, of course, was interest-group politics: realistically, given the insurance industry’s power, Medicare for all wasn’t going to pass, so advocates of universal coverage, myself included, were willing to settle for half a loaf. But the fact that it seemed politically necessary to accept a second-best solution for younger Americans is no reason to start dismantling the superior system we already have for those 65 and over.

Now, none of what I have said should be taken as a reason to be complacent about rising health care costs. Both Medicare and private insurance will be unsustainable unless there are major cost-control efforts — the kinds of efforts that are actually in the Affordable Care Act, and which Republicans demagogued with cries of “death panels.”

The point, however, is that privatizing health insurance for seniors, which is what Mr. Lieberman is in effect proposing — and which is the essence of the G.O.P. plan — hurts rather than helps the cause of cost control. If we really want to hold down costs, we should be seeking to offer Medicare-type programs to as many Americans as possible.