DW and I evaluated LTC policies, since both of our fathers had benefited from them. They used to be a lot cheaper, the insurance companies found they had to pay out a lot more on these than they expected so now they aren't very attractive. You spend something like $50-80k over the years to get $200k of coverage; for that payoff, we'll just self insure, we should accumulate about that much from saving that premium money ourselves, and will have fewer restrictions on how we can spend it. A lot of those polices will only pay for caregivers through a company, for example, and both of our fathers at times got help from "informal" caregivers for much cheaper.
With no kids, though, we are worried. Both of our parents could not have stayed as long as they did in their houses without us kids visiting and taking care of some things. We do plan to move out of single family type housing eventually though, and are saving up enough to pay rent and, later, assisted care expenses in our older age. We expect to need $500k or so for that. The paid off house idea is nice, but taking care of it turns into a lot of money when you can no longer safely change light bulbs in ordinary ceiling lights (my MIL in her 80s), for example, let alone mow grass or shovel snow.
We also plan in the next 10 years or so to start more seriously looking into "group housing" type situations, especially ones where there are some variety of ages and people help each other out according to their capabilities, as opposed to paying staff to do everything. Those are increasing in popularity, and tend to be much cheaper than ones where staff does everything. I think a key is to not be as wedded to "aging in place, no matter what" as our parents were.