Curiously, the stat adders (along with bonuses scaling so high) actually killed off another thing that I liked about 2E which was the ability to play an effective character with weak startng stats.
To the contrary, I believe that the 3e approach got rid of the problems that came with low starting stats.
In AD&D, if you started with a 15 or 16 INT as a Wizard the highest level of spells you could cast was already set and you'd never be casting 9th level spells, end of story, and you also had a total cap on the number of spells you could know unless you had a 19 INT so it could be quite possible to have your character's spellcasting permanently cap out long before the end of the campaign. With 3.x as long as you started with a 15 you'd never be unable to cast your highest level spells, even without stat boosters, just by raising your scores as you level, and they got rid of the maximum spells known per level.
The uniformity of constitution bonuses to HP meant that there were real reasons for characters other than Fighters, Rangers and Paladins to have a high CON score. Yes, a Wizard or Sorcerer with a 20 CON getting 1d4+5 per level might not need good rolls as much, as they would otherwise, but that's compared to them getting no difference from a 18 CON as a 14 CON (especially with no bonuses to saving throws from a high CON until 19 in 2e IIRC, there really was little mechanical difference for a nonwarrior to have an above-average CON score aside from System Shock and Resurrection Survival chances).
In AD&D 2e you only needed a 9 STR to be a fighter or a 9 DEX to be a Rogue, the biggest direct aid you got from high ability scores was the XP bonus for a high prime requisite. In 3.x if you for some reason wished to play a rogue or fighter with middling physical stats, you could have that character gain significantly throughout their career, as opposed to the AD&D way of hoping to find Wishes to ramp up your scores and that's pretty much it.
Well, there were strength-boosting items, but no items for other ability scores and the game was very heavily intended to make it so you could never outright buy magic items and having to permanently spend a Constitution point to make magic items other than potions and scrolls meant that PCs never, ever wanted to make magic items, ever. They might not have gotten as much benefit from their CON score most of the time, but they didn't want to trade a time they could be resurrected (and the odds of it succeeding) for a party member to be able to hit harder. In my experience, magic items in most campaigns were rare until 3e with even parties in their teens having maybe one or two items per person, and they were randomly determined so you weren't likely to get really useful items like Gauntlets of Ogre Strength, and only the fighters having magic weapons (and often having to quest and beg/bargain/steal to get those), but of course YMMV.