Stops??? Who told you that? I know plenty of elderly people who supplement Medicare with private insurance. There's no reason to stop that. Medicare is a social safety net.
It is still not “pure” health insurance. The taxpayers pick up much of the cost, emergency and hospital healthcare, part A of Medicare.
Not comparable to property and casualty or term life insurance, where an unlikely event is insured. I would say those are closer to insurance rather than cost sharing / taxpayer subsidy agreement like health insurance is. And whole life is an investment / tax savings product.
Health insurance also stops at age 65 and becomes a taxpayer funded program (Medicare).