Lanefan
Victoria Rules
Heh - on reading your first line I was about to suggest 2 classes per score; and then I saw the second line where you suggest three. So I'll take the average.Since D&D used 6 attributes, I would prefer if there was at least one class pre ability score.
Ideally I'd go 3 classes per ability score just for variety's sake.

The one thing I'd add to a two-per-score setup would be a couple of classes that kinda need at least three or four good scores if not more in order to work well. Once that's done, we end up with a rather 1e-like class list at 2 per score:
STR - Fighter, Cavalier
INT - Wizard, Artificer*
WIS - Cleric, Druid
DEX - Thief, Assassin
CON - Ranger, Barbarian
CHA - Paladin, Sorcerer**
ALL - Bard, Monk
* - Artificer can be replaced with Illusionist, Necromancer, or some other arcane class for a more 1e-like feel; [ETA] or psionicist.
** - Sorcerer can be replaced with a Cha-based arcane class e.g. Necromancer if you don't want spontaneous casting in the game.
And yes, the idea here is that Bard and Monk are gated behind some rather strenuous stat requirements across the board in order to make them less common.