If it is fair (and considered playable) for a character to have below standard STR (or any other stat), then INT should be treated equally. Implications for INT could be caused by:
1) cultural or rank based dietary restrictions, whether as an adult or a growing child (lead in sweets or paint, lead goblets [cf: Roman Empire], Mrs Ploppy's sausages, alcoholic, the gas at Delphi)
2) disease that directly affects brain or cranial development (plenty to choose from, in addition to many types of general infection that indirectly affect the brain, as well as some parasites)
3) failed to perform any mental exercises, either from laziness, religious observation, tribal superstition, social convention and peer pressure, and so on (also sports, boxing)
4) hit by a bus, dropped as a baby
5) deep psychological impairment, psychosis, mental stress and breakdown
Given that the core "playable nature" of characters is often based on their ability to reason and make choice as a mental conduit for the player (even when role-playing the fool or village idiot) then it almost makes sense to have a minimum INT for player characters (playing a paraplegic has greater potential than playing someone who is brain-dead [unless playing a psychic or POW-based game). Even so, any degree of disability would (in general) be equally debilitating when comparing stats.
If I do use 2d6+6 for INT, the underlying reason differs in that it isn't for a smarter species average.