My take on this is that when something has a probability between 35 and 50 percent, it is not an insurable event. Basically, every family needs to save up for long-term care needs in old age. Insurance covers rare events, not events that are this likely.
My wife and I have long-term care insurance. The reason I think that makes sense is that we are not over 65. If one of us should require long-term care in the next several years, that would be expensive. It also is unlikely, at least compared with the probability that we will require long-term care when we are over 75. So it is an insurable event.
In my view, long-term care is an insurable event only for people who are under 65. After that, it becomes a matter of personal saving. Thus, what most people think of as long-term care insurance (covering people over 65) is simply redistribution of wealth from people who save for their old age to people who don't. Thus, it is bound to be undertaken by government rather than the private sector