Believe me, it doesn't. I have a number of old school non-concaved bats that pick up just as well as the similarly weighted concaved bats. It's all in your head!
I meant that it does as you are removing weight off the bat, the pick-up is enhanced, but I guess if we are comparing it to bats of the same weight, then yes, pick-up isn't really improved by concaving at all. I agree about the old school bats, (Small edges, no concaving and meat in the centre of the bat) in that the best pick up I have had was a 2.11 Mjolnir, which picked up just as well as my 2.8 bats, which is why I am more keen traditionally shaped bats.
Also much more responsive, but that's not to say concaved bats are bad!
I'm not sure who it was that said more meat down the centre of the bat rather that the edge improved pick up (I think they may have said bat speed too), but it has been the case for most bats I have used. Something related may pop up in a class sometime in the future, so may shed more light into this area for me.
Or I could just drop out and become a podshaver and experiment to find out.