I currently have 5 Basses with the P/J setup but the bridge pickups are disconnected. I've never liked bridge pickups in any of my Basses over the years. I've never really liked traditional humbuckers in Basses either as they sound muddy. IMO, Leo got the split P pickup right when he put it in the Precision Bass. It's a noiseless sigle coil that is on so many famous recordings. I love that full tight tone.
I had never owned a Jazz Bass until a year and a half ago, I got a Geddy Lee. I ordered a EMG JVX Set that sound like Passive's on steroids. They are very dynamic like a passive pickups but have the extended lows and highs. I left the bridge wired up but don't use it much at all. Yep, my Jazz bass pretty much sounds like a P Bass, LOL.
Seems everyone likes what they like as far as tone and it seems and I think it has a lot to do with what you are use to. Thank God there's so many choices to choose from on the market today.
If you like the sound of a Jazz Bass using both pickups and that makes your boat float better, than by all means, stick that jazz pickup in the sweet spot.

