@ Mujus, I've always felt that yes, while the use of "he" as a gender-neutral singular pronoun does speak on some level of underlying sexual inequity within our culture, it's so inanely academic as to be irrelevant to most members of the equal rights movement, who (I would hope) recognize that there are more pressing issues to tackle before we start discarding practical tools of language (particularly in the absence of suitable alternatives). Your suggestion of changing sentences like, "Every child should bring their notebook" to, "All the children should bring their notebooks" strikes me as a decent method to avoid taking a readily identifiable stance on the issue altogether, but it's not a fix applicable to all situations. I concede that, "Every child should bring his notebook" DOES sound a bit awkward, but I'd argue that it's only generally perceived in that way due to the rarity with which sentences are formed in that manner, not by any inherent "flaw" in their construction.
Aesthetic preferences aside, I think it boils down to the avoidance of ambiguity. Using "he" as the rules of grammar prescribe is the best way to convey thoughts involving gender-neutral singular third person pronouns that our language has to offer. Everything else is a compromise, and a compromise of understanding.