Long term care insurance is a bet, it may pay off and it may not. But at some point your parents will become uninsurable--age or even a hip fracture can do this, so the decision will be made for you eventually.
Home care by children alone rarely works. I think that most people (me included) grossly underestimate the unrelenting physical and emotional burden, and the ones closest will become overwhelmed and burn out, even with all the love in the world.
Otherwise I think that preparation is a matter of personality. My mother is still alive and well, so I make sure that I retain some flexibility for emergencies, as well as maintaining her resources and mine if things head south. But I won't plan for every contingency, much less agonize over them. For all the statistics and probabilities, there will be only one course in reality, and I dislike spending time and energy planning for things that (1) may never happen, and (2) if they do, the chances of the preparations being timely and adequate are remote.
The best thing I and my sister have done is to rehab and declutter her house, taking our time and doing it inexpensively. Not only does this remove a future burden from us, it makes the house saleable if it comes to that, and in the meantime she gets to enjoy it while still alive and well (for me this is most important thing). This seems to be the best preparation for whatever happens.