H&P's CGEL (p. 427) says this about one:
One differs from the core 3rd person personal pronouns in that it cannot be used as an anaphor to another NP: *A̲ p̲o̲l̲i̲t̲i̲c̲i̲a̲n̲ shouldn’t take o̲n̲e̲s̲e̲l̲f̲ too seriously. Indeed, for some speakers (primarily AmE) one can itself be the antecedent for a personal pronoun anaphor:
[4] i %What is o̲n̲e̲ to do when h̲e̲ is treated like this?
ii %O̲n̲e̲ should do t̲h̲e̲i̲r̲ best to ensure that such disputes are resolved amicably.
Examples like [i] are now less common than they used to be, in line with the general decline in the use of the purportedly sex-neutral he. Type [ii] is quite rare: singular they is not well established as anaphor to one.
As evident from these examples, one is neutral as to sex, but that is not the most significant respect in which it differs from the 3rd person singular pronouns in [2] (and hence it could not be fitted into that system as a fourth gender). For most speakers one is used only non-referentially – in talking about people generally rather than in reference to a particular individual. It is in competition with the non-referential use of you, as in What are you to do when you are treated like this?, and so on. One belongs to a more formal style than you, and of course makes clear that there is no reference to the addressee in particular (as there could be in You shouldn’t take yourself too seriously). There are speakers, however, who in certain contexts use one instead of I to refer to themselves: %One suddenly realised that one was being followed. This usage is associated with upper-class BrE – and is regarded by many other speakers as pretentious.
(In CGEL, symbols * and % indicate the following example is "ungrammatical" and "grammatical in some dialect(s) only", respectively.)
In a nutshell, this is what CGEL says here:
Some speakers can use he or they to refer to one, but they're in the minority. And one is a formal version of the generic you, both being used only non-referentially.
And I notice both one and the generic you are uniquely capable of referring to the same entity as did their earlier instance while still maintaining their non-referential nature. This unique capability, however, is not found in someone. That is, someone cannot refer to the same entity as did its earlier instance while still maintaining their non-referential nature. Hence, the ungrammatical *Why should s̲o̲m̲e̲o̲n̲e̲i cook s̲o̲m̲e̲o̲n̲e̲'si own food? and the question:
Is there a reason that one gets this odd treatment while other generic pronouns that contain one (e.g., someone) don't need to obey that rule?
I don't know what you mean by "other generic pronouns". For example, someone, is not as generic a pronoun (if one follows traditional grammar) as one, much less I, you, he, she, or they. In fact, someone is, to quote @Araucaria - Him,
[a compound] where the first morpheme acts like the Determiner in a noun phrase and the latter like the common noun Head. In other words [someone behaves] like a whole noun phrase where the two parts of the noun phrase have become joined together.
Therefore, someone is semantically and syntactically similar to, but only morphologically different from, less idiomatic some person. And the latter lacks the above-mentioned unique capability:
*Why should s̲o̲m̲e̲ ̲p̲e̲r̲s̲o̲n̲i cook s̲o̲m̲e̲ ̲p̲e̲r̲s̲o̲n̲'si own food?
So it's understandable that someone is just like some person in that it lacks the unique capability, isn't it?