I've always felt D&D Intelligence is best characterised as formal education. Most of the skills lean that way (except Investigation), as do the classes.
The implication that Barbarians, Monks and Paladins are never smart, is, when you think about it, pretty damn obnoxious on it's own.
(And if the game is basically placing limits on my characters intelligence based on whether they're sterotypical nerds or jocks then it's a much worse game then it needs to be.)
Doing, it that way also puts a limit on the stupid characters, which regardless of whether they're actively offensive or not, are usually incredibly tedious to everyone else at the table.