While I really do tend to lean in the direction you suggest, I don't think it's quite a cut-and-dry as you claim. Here are a few things to consider.
First, we're only talking about language. We get those gendered pronouns not because of a need to distinguish between how a person views his gender (or how the world views it), but because of stupid linguistic convention going back to English's Indo-European roots. You'll see that in many languages in the same family, nouns all have gender, even absurd ones like "airplane" or "shoe". These genders have absolutely nothing to do with sexual identity, they're essentially randomly assigned, conferring no additional meaning (but providing a parity check in communication, helping ensure clear transmission). Coming from this history, we shouldn't be too concerned with the way pronouns correspond to individual humans.
Second, I don't think it's hard to imagine socially-undesirable consequences of honoring anyone's own claimed gender. I'm thinking of a biological-male claiming to self-identify as female, so that he can use the women's locker room at the gym. So under what circumstances do we want to honor their self-image (or, for that matter, to believe their claimed self-image)?
Third, with identity politics still having legal bearing in our system, it seems that self-identification of gender may derail efforts to ensure gender equality. Given that there are legal structures in place to protect females, may I (as a biological male) claim to self-identify as female, and achieve those same protections? May I at least self-identify on official forms (thereby making enforcement of workplace protections unenforceable)?
Not that these things are insoluble, but I think that we need to give thought to the repercussions should we choose to take any person's claims of gender at face value.