Deferring SS to age 70 is the lowest cost longevity insurance I know of.
I don't want to lock in on any kind of annuity right now at these low interest rates. If rates go back up I will reconsider. An SPIA is widely touted here as the least confusing and lowest expense kind of annuity. So far my light research on this agrees, but I plan to do more. At 59 I may be too young to buy an SPIA optimally anyway.
I haven't heard of any where the payment doesn't kick in until 85. You'll have to fill us in on what kind of longevity insurance you are looking at. My understanding is that you can set it up to turn it on annuities whenever you want, but again my research is light. I know my dad has one that he can decide whenever to turn it on. It has a life insurance benefit so that's a benefit of not collecting now. But I think they are going to cash it in since it is beyond any surrender fee, and they need more money for memory care now.
I can't speak for anyone else, but I feel that my family history is good and my health is good, so some longevity insurance is probably worthwhile. If I die early, oh well, my son won't get quite as much, and I'm sure I have enough to handle a shorter retirement, so losing the annuity bet won't sink me. But the insurance could be helpful with a longer life span. Maybe it would work against you if your LTC strategy is Medicaid. I don't know how that would factor in but it's something to look into before buying.