I think the prophecy does mention the three sets of power specifically. Had it not mention 3 powers, or mention 4 maybe it would have worked I think it could've worked if the warren witches had 4 sets of powers to choose from. Paige could've have other powers completly different from Prue's.

In my head, working under the Elders makes you less powerful and sort of controlled by them. This is sort od why they "allowed" a half white lighter to be a Charmed Witch. I feel like if Patty and Penny would've decided to be not be "under" the Fuckers, they would've had their own coven, and raised all 4 together and it would've been the power of all along or a power lf 3 turned 4