You definitely don't NEED one.
That being said, there are many people that prefer the benefits of not having to rely on Disney Transporation. We find that we generally save the equivalent of one extra vacation day by renting a vehicle. That being said, we love to park hop and make dinner reservations all over the place.
Because you are staying at BC, you won't save any time on getting anywhere except for Animal Kingdom, the waterparks or Downtown Disney. While Magic Kingdom might seem like an area where you could save time travelling to because you otherwise have to wait for a bus, you would still need to drive to the TTC and transfer to a monorail or boat, so any time savings there would be neglible.
You will save time hopping between parks and driving to other resorts if you rent a car. You also would have the flexibility of travelling off-property, which offers several meal and shopping opportunities.