Wizards, who only really have their spells, rely on the potency and offensive capabilities of their magic. They need as many spells as they can get, with as much effect as they can get, because if they ran out of spells, they're not much more than a commoner with better equipment.
That's why wizards will usually have a very high int score, with the other scores lacking behind quite a bit. Sorcerers are similar, of course, with their charisma.
Clerics, on the other hand, will often get away with lower scores. Most of their spells never involve saving throws - they're just there to increase the clerics capabilities (or heal people). Beyond the spells, a cleric isn't that shabby in melee (which is only improved by his magic). So you'll often see a cleric with Str, Con and Wis comparatively close to each other.
I'm not quite sure about the minimum ability rule myself: On one hand, it is a virtual ability requirement, something 3e has otherwise done away with (no more "paladins must have cha 17+" nonsense). On the other hand, it is obvious that the key ability score should have some impact to spellcasting. High scores grant bonuses, so low scores should impose penalties.
Let's think this on:
High ability scores usually grant a numeric bonus - Str 14 means +2 to attacks. Int 14 means DC 10 + 2 + spell level. This would be easy enough to adjudicate. So the Wizard with int 9 would cast DC 10 -1 +3 fireballs, for a DC for 12.
But there's another benefit for high ability scores: Extra spells.
Right now, there's a sort-of formula to determine bonus spells (it's easier as a table). You could get rid of minimum scores, but then you would have to change that that table to accomodate negative modifiers and spells. So if you are not smart enough, you get less spells than the spells per day table suggests!