A human rogue in P6 in Classic that is in near-BiS, unbuffed but with enchants, is at about 1300 AP.
If you strip all the AP from the gear, you lose about 560 AP. If you also replace all enchants that give AP or strength with the best agility enchants possible for that slot, you lose about 75 more AP. You’re now down to about 665 AP; this is less than a BiS-geared rogue in P1.
If you want to take that P6 near-BiS geared rogue and add that 665 AP back to the gear as agility, this rogue - which has ~32.3% crit and ~31.6% dodge with 365 agility, and gets 1% crit per 29 agility, 1% dodge per 14.5 agility - that rogue is now sitting, unbuffed, with ~55.2% crit and ~77.5% dodge.
So, no; not even rogues or hunters go purely on agility. They require AP as well, just like casters need both int and SP.
I’ve already quoted myself as to why int giving SP is not a good idea with Classic’s stat design. If you want to bring up shamans, I’ve mentioned that as well in this thread. It’s by no means a solution, but both the OP and myself have come to the conclusion that trying to pump both melee and magic stats as a shaman - short of a rune being implemented that converts a portion of AP to SP - is absolutely horrible with Classic itemization.