Strange Thoughts on Experience Bonuses

From the very beginning, the rules of Dungeons & Dragons rewarded high scores in a character's prime requisite with a bonus to earned experience. Although the actual implementation of this rule varies from edition to edition, it has been present in every version of the game published by TSR. It's also present in Empire of the Petal Throne, which is hardly surprising, given that its rules are derivative of those of OD&D. As originally presented in 1974, the rule provides the only explicit mechanical benefit to having a high score in Strength, Intelligence, or Wisdom, each one of which was associated with one of the three character classes (Fighting Man, Magic-User, and Cleric, respectively). The other three abilities – Dexterity, Constitution, and Charisma – have other mechanical uses (however ill-defined in the case of Constitution). 
Supplement I changed all this, first by introducing the thief class, whose prime requisite was Dexterity, and second by beefing up the mechanical benefits of most of the other abilities (the main exception being Wisdom, which remains solely "an experience booster for clerics," in the words of Gygax). These changes, which were carried on and even expanded by later versions of the game, began the process that ended with the claim, in the AD&D Players Handbook, that it is "usually essential to the character's survival to be exceptional (with a rating of 15 or above) in no fewer than two ability characteristics."
After lots of thought on the matter, I have made some measure of peace with the idea that ability scores should be mechanically important. If not, what's the point of even generating them? However, I continue to worry that, by making high scores in abilities mechanically beneficial, there will come to be an expectation that, as in AD&D, most characters must have high ability scores. In that case, we get a variation on the previous question: what's the point of generating ability scores at all if every character needs to have high ones? 
The question becomes even more relevant when one considers that, as written, characters with high scores in their prime requisite not only reap immediate mechanical benefits from those scores (hit and damage bonuses, higher hit points, etc.), they also advance faster in their chosen class, thanks to the bonus to earned experience. To my mind, this makes high ability scores so attractive that I wonder why any player would not deem a character with any sub-optimal abilities "hopeless" and roll up a new one. Consider, too, the increasingly absurd lengths to which AD&D went to ensure that all player characters were exceptional in their ability scores.
As is so often the case these days, I find myself taking inspiration from Chaosium's RuneQuest. In RQ, there are mechanical benefits to having a low score in at least one ability. I very much like that because that benefit comes at a cost; there's a trade-off between two clear mechanical goods. I'd love to see something similar in D&D and derivative games, something that provides some incentive not to have high scores in every ability.
That's why I have a strange idea: what if, instead of granting an experience bonus for high ability scores, one granted them for low scores? On some level, this makes intuitive sense to me. Would not a character whose native abilities were already exceptional learn less from his experiences than a character whose abilities were below average? Further, I can't help but feel that granting an XP bonus to a high score, which already grants clear mechanical benefits, is gilding the lily, so to speak. If the goal is to keep the random rolling ability scores and encourage players to keep the scores rolled, does it not make sense to provide a "consolation prize" to low scores?
I am sure there are problems with this idea and, if so, I expect my readers to point them out in the comments. From my current vantage point, though, I think this is something to be explored, both from a purely game perspective and from the point of view of learning through experience.