It's worth reminding yourself that a family history of Alzheimer's (or other types of dementia) is not
your destiny.
I write this as a guy whose father died of Alzheimer's 15 years after his father died of Alzheimer's.
Genetics loads your gun, but lifestyle has a big hand in squeezing the trigger. There are genes which kickstart early-onset Alzheimer's as early as one's 40s (especially in a particular South American village), and there are genes which kick in for late-onset Alzheimer's (typically mid 70s). However there's also a gene which genealogists know is protective against Alzheimer's, although geneticists just can't pinpoint it on the genome yet.
There are plenty of elders whose (autopsied) brains were full of the pathology associated with Alzheimer's... yet the elders did not actually have Alzheimer's before they died. Either something else killed them first (cardiac, cancer) or something in their genome kept Alzheimer's from kicking in. Or maybe it was just high-quality whiskey.
You could buy LTC insurance if it makes you (and your family) sleep better at night, but this is also the opportunity of a lifetime (literally) to practice those Mustachian diet & exercise habits. Frankly I'd rather pin my hopes on lifestyle rather than in a life-insurance company.
Also, does anybody know what happens if an insurer decides to withdraw from the LTC market? What happens to all the premiums you've paid? Do they vanish into thin air, or would they be refunded?
The companies just stop issuing new policies, but they've contracted with you to provide your insurance.
Rate increases can happen where permitted by the policy and by your state's laws. You can cancel the policy if you want to, but insurers can only modify it with the permission of your state's insurance commissioner. Of course they can also deny coverage (that happened to my father) but you can pursue an appeals process. You essentially show the insurer that it's cheaper to approve the claim than deny it.
Once an insurer withdraws from the market they might also be free to sell the policy to some other insurer, but the original terms (and approved premiums) remain in the contract. My father's LTC policy was sold to two different companies before it ended up with John Hancock (through mergers & acquisitions).