It's an interesting question, but the last batoff actually had a bat that answered your question.
The GM Icon we used weighed more than 3lb. All of the testers agreed that it picked up really, really well. If you go and watch the videos, you can see that universally, everyone had problems playing the ball properly because they couldn't swing the bat through in time and were late with their shots.
What does this tell us? When you play a shot you use gravity and your muscles to get the bat in the right place. If the dead weight of the bat is too heavy for your mechanical systems to overcome the inertia, you cannot play the ball properly. Even if it picks up really well, you still have to use an amount of force to generate momentum with the bat, so a 3lber that picks up like 2lb10oz still requires the force needed for a 3lb bat to move it in the right direction.
What am I saying? Pick-up is how we feel with the bat. If it doesn't pick up how we like we won't feel comfortable playing our shots. Dead weight affects our ability to move the bat to where we need it. If it is too heavy for us then we will fail at this, and no matter how well it picks up, we won't be able to play properly with it.
For me a range of 2lb9oz to 2lb13oz fits the bill and anything heavier starts to incur a cost with me being late to the ball.