D&D With No Ability Scores

The 3-18 ability scores have been around since D&D's inception, but I believe their original purpose has become so distorted and, honestly, taken for granted, that I truly think an old-style game (not necessarily in rules, but in spirit) that uses the 3-18 system can never live up to its potential, simply because, as role-players in general and D&D players specifically, the 3-18 ability score range has become so ingrained in our minds that it is inseparable from all of the excess baggage that the game has accrued over the years.

So when I finally begin running my old-school game in a couple weeks, I'm ditching ability scores. Well, not entirely.

Characters still have six scores: Strength, Dexterity,Constitution, Intelligence, Wisdom, and Charisma.
Players roll d12+d8, in order, for each score, and then compare the results to a table to find the ability modifier:
2-3: Poor : -2
4-7: Below Average : -1
8-12: Average: +0
13-16: Above Average : +1
17-19: Exceptional : +2
20: Superhuman : +3

Players may swap any one pair of results. In situations where chance is involved, players add a given ability modifier to the die roll. Attack rolls and saving throws are functions of class, and thus not affected by these modifiers.

The table is weighted in favor of average and lower-modifier scores (+/-1). I'm getting rid of ability score prerequisites for character classes, but I still wanted that "feel" of the older editions, where high ability scores were still special. However, a character with low scores isn't hopeless, because the two most critical rolls in the game (attacks and saves) remain unaffected. A fighter with exceptional strength has the advantage in bending bars and opening gates. However, he is no better at attacking than a fighter with average strength of the same level. Although the fighter with superior strength will cause more damage (the mod is added to damage rolls), statistically he will hit an opponent no more often (magical equipment and other enhancements notwithstanding).

I'm looking forward to seeing how this system works.