The "base 4" classes should be individually dependant.
And lo, it came up from the basement of the Gygax that the Fighter shalt need their Strength, the Magic-User shalt need to be smart, e'en as the Cleric needs be Wise, and the Thief shalt forever be Dextrous. And the Gygax smiled his countenance upon them and said it was good and so good it was.
This, then, allows the player oodles of room to devise a character by applying their other higher scores to various abilities, as desired for their concept. Make the Dextrous, agile fighter guy, the intelligent charismatic leader fighter guy, the sneaky thief whose extra tough from their time in the gutter, or the mage who packs a serious punch...with their fists!
As you move into the [what once were] "sub-classes" of those 4 categories, the need for specific abilities increases, as the special abilities/powers/skills of those classes increase. It is logical, offers a degree of built-in "balance" for those that require it...and has a certain symmetry I find appealing.
So, those how about we call them "next strata"
TM of classes [instead of "sub" so folks' panties don't get bunched with the connotation that they are somehow "less" than the base classes. Ok? Ok.] I would make have 2 minimum requirements. A la...
Assassin: Dexterity (as a "next strata"-Rogue) and Strength (for overpowering or holding their own against targets/getting "the job" done).
Druid: Wisdom (as a "next strata"-Cleric) and Constitution (for shapeshifting and enduring the wilderness).
Sorcerer: Intelligence (as a "next strata"-Mage, which is pushing it imho since I think it's better served as a "tradition" or background, not its own class. But that's a debate for another thread...and under the bridge at this point) and Charisma.
Ranger: Strength (as a "next-strata"-Fighter) and Intelligence (or Wisdom, whichever the majority of their skills are based on) or Dexterity (for extra swifty archer or melee guy).
Warlord (while I'd prefer it a theme/specialty, we know it's in, so...): Strength (as a "next-strata"-Fighter) and Intelligence (for tactical leader guy) orCharisma (for inspiring leader guy)
Then there are the "
next next [third] strata" after that, the "rare" type classes with exceptional extra abilities. A la...
Bard: Dexterity (as a "third-strata" Rogue) and Intelligence (for spell-casting) and Charisma (for all of the interactions stuff)
Paladin: Strength (as a "third-strata" Fighter), Wisdom (for the clerical abilities) and Charisma (for being all shiny paragony).
Barbarian: Strength (as a "third-strata" Fighter), Constitution (cuz they's a Barbarian!) and Dexterity (cuz Barbarian's are super good at all things physical). I suppose case could be made to place Barbarians in the second strata with just Str. and Con.
Monk: Dexterity (as a "third strata" Rogue), Wisdom (for the mystical stuff), and Strength (for the acrobatics and unarmed fighting stuff).
Warlock: Intelligence (as a "third strata" Mage), Constitution (for personally containing/channeling their arcane power) and Charisma (for interactions and probably had something to do with gaining their power in the first place, possibly also flavored for using their powers).
And so forth...Shamans, Sword-n-spell guys, Psions, whatever else they come up with.
Sooooo, what was the thread about again? Oh yes!
YES! Classes beyond the base 4 (which would be MOST classes) SHOULD be dependent on more than one ability. I would be averse to making more than 3 (perhaps 4 for 1 or 2 of them) but I have no problem with "MAD" classes.
And, as others have said, ALL ability scores are (or should be) important, if for no other reason than that elusive "RP" in the "G" so many seem to forget about or demand/require mechanics attached to the score in order to give them meaning.
--SD