Thank you, yes, this bothered me too! I figured I'd read every thread to make sure my post wasn't redundant, and it looks like it would have been. But I want to give the example too:
"It eats its dinner" vs. "Somebody eats somebody's dinner."
I think it'd be a bit harder to argue that the second sentence above should use "somebodys dinner." (This comparison of "one" to "somebody" was, sadly, not my idea - but I think it's a smart one)
Personally, it seems the English language more and more requires a neuter singular pronoun to play opposite "they/their/them/theirs(etc.)." Common usage has "one" taking that role, along with "he/she," "hir" (and other awkward portmanteaus), "it," and even "they" and "you."
There are two perspectives when considering grammar: descriptive and prescriptive. Descriptive grammar accepts "common usage" as a legitimate source - encourages it, even (and now I'm quite happy to have that source - thank you Panjandrum for the Ngram referral ). Communication is defined by the speaker and listener, and as an extension of that, words and grammar need only follow the rules that allow for understanding. I don't think we are talking about that sort of grammar here though, since otherwise one could just say "he ate his dinner" or "they ate their dinner," and in context, the gender, general/hypothetical quality, and singular quality of the "he" and "they" could still be communicated by context. In other words, "ones" and "one's" are equally acceptable simply because they are both easily understood in context.
As for prescriptive grammar: I couldn't find a good source that specifically says "it/its/it's" is specifically an exception to the possessive "'s," nor for one that states that personal possessive pronouns do not use the single apostrophe, and instead have idiosyncratic possessive versions. The latter rule seems to me to be a bit more inclusive, but if anyone has a good source for either, I'd love to see it. Also, if anyone could somehow make "one" a personal pronoun, as I believe it should be, I'd be disproportionately, irrationally happy...though I suppose that's just crazy-wishful thinking.