I tend to agree with what I think is your practical conclusion, that cryonics (over a long period of time) will not preserve that which is most important, and that for most people it's at best unobvious that cryonic preservation is desirable. However, I disagree in how I get there.
You think there are facts of the matter about personal survival, and that a reanimated frozen corpse does not survive as the same person who died. Those who endorse cryonics typically (but not always) deny that there are such facts, but then they behave as though there are! They place great values on their memories, personalities and patterns of thought which go far beyond what could be justified by an objective appraisal of their use or importance in the far future - the criteria they would presumably use in assessing the value of cryonic preservation of a stranger. I think people should apply those same criteria when thinking about whether to preserve themselves.
I don't think there are facts of the matter about personal survival after cryonic preservation, but this 'cuts both ways'. Yes, it's "exactly as though you went under a general anaesthetic and later woke up". (I don't say it's exactly the same as going to sleep and waking up because I think the mind is still 'doing things' throughout sleep.) But it's also "exactly as if you died and someone else woke up in your place".
Now for a hypothetical: imagine that the technology for restoration of cryonauts has been perfected, such that when the person is reanimated they feel as though they have just 'woken up' after an ordinary spell of unconsciousness, and have the same personalities as before. Suppose that, for some reason, you are dying in a remote place and the only way 'you' (a person with your body, your memories etc.) will be able to persist is if you're cryonically preserved in a local hospital, taken to a much fancier hospital and then thawed out a few hours later. I think that if such circumstances were routine then, as a matter of fact, people would regard cryonic restoration as being exactly like coming round from a general anaesthetic. Abstruse metaphysical considerations would evaporate before the manifest fact that people are surviving cryonic preservation (in the prephilosophical sense that 'people survive anaesthesia'.)
In other words, the quest to prove (or demonstrate the unprovability of) the fact that a restored cryonaut is 'the same person' as the person who died would be compartmentalised as 'the kind of thing only a philosopher would care about' in much the same way as 'brain in a vat' skepticism, or whether other people have minds; whereas "we all know" (or at least we behave as if) the common sense answers are correct.
(However, "common sense" might be very different if a restored cryonaut had cognitive deficits or personality changes like one sees in cases of frontal lobe damage.)
I'm currently trying to convince my parents to sign up for cryonics.
The problem is that they are completely opposed to the any form of life extension and/or immortality (and that’s without even mentioning something as "strange" as cryonics). Unfortunately, being their child, I have the intrinsic property that I can never know more about life then they do. The only thing they will believe are scientific studies from respectable scientists (a respectable scientist being someone who only says what they want to hear and is not me)
I have the arguments I gathered from Less Wrong and the Alcor Library. I’m focusing on my mother since my dad is impossible to convince without her support.
Her argument is that when you live for a very long time/forever wars are almost guaranteed to occur at least once in your lifetime and she doesn’t want to live through those. I asked her when, given that we could perfectly predict the future, we would know a war would break out tomorrow she would commit suicide today. Her answer was yes, as she couldn’t bear losing any of us and doesn’t want experience a war. I pointed out how I would feel if she died but she just dismissed the entire thing as crazy.
My parents aren’t religious at all, so that’s one less bridge to cross but for all the rest I would greatly appreciate anything that might help convince them.