Can't remember exactly where I read this, but somewhere it was said that Rahkshi of Heat Vision only were the most numerous kind of Rahkshi around during the battle of Bara Magna. So there actually were other Rahkshi kinds around, too.
And the Rahkshi's staffs only enhance their power - much like a Kanohi does a Toa's. The staffs aren't the source of a Rahkshi's power (rather it's the Kraata, I'd say). Rahkshi without a staff are greatly weakened, but can still use their powers.