This is an interesting discussion for me because I just dealt with this.
Before I get started, I just want to comment that I'm surprised to see so many of you are like me – switching from Fender Jazz to MusicMan… But that’s not the point of this discussion.
On my Jazzes, I always rest my thumb on the pickups. When I switched to the SR5 a couple years ago, my pickup would not lock (it floated), so putting my thumb on it messed up my sound. Even though I locked the pickup with some lock-tight (discussed in another thread) to solve that problem, I began to use my b-string for my thumb. In hindsight, this was a terrible habit to form. My playing became terribly sloppy and I found myself on a plateau. I couldn't get any better, and I had become frustrated.
Last month, I picked up a rudimentary book as I do from time to time and I saw the discussion on resting the thumb on the pickup. "Oh yeah!" I said. That night, I put my thumb back on the pickup. Eureka! I found it!
Reclaiming my pickup for the thumb rest has completely changed my playing style. I no longer have to struggle wondering if I'm going to pluck the wrong string because now I know the string intervals without having to look. It also changed my plucking style. I used to dig hard into my strings, which I never really liked, but that was the way I tended to play. Now, I pluck much more gently. I have actually changed the stroke of my pluck. (This conversation in any other forum than this one would sound so dorky!) As a result, I've been able to lower my strings, and I can play TONS faster than before.
That's a lot of change that I attribute to one thing: placing my thumb on the pickup.