Here are a few observations.....
Marketing - There just isn't a market for this. I'm going to lump this in with the "Why doesn't Fender offer a five string J bass with wide string spacing in purple burst African stinkwood?" If there were a market for it, I assure you, it would be out there. I am a capitalist. Many corporations run on the capitalist system. Profit is good. If there were any profit in it, somebody would be doing it. Also, Ampeg and others have tried it on guitars and basses. Amp companies have tried the "modular" approach to amps, allowing you to swap out preamp sections and even power sections (Randall and Markbass come to mind first). None of these things sold/sell well. If they did, everybody would be on the bandwagon.
This would also require MASSIVE cooperation between companies. Let's just say a major pickup manufacturer released a system like you describe. We'll go with Duncan because it's easy. For this to take off worldwide, EMG, Bartolini, Nordy, and everybody else would have to adopt "The Duncan System" for it to be accepted. Why? Because people like you would not be satisfied with only being able to swap Duncan pickups. These companies are not any more likely to do this than Ford is to start building engines in a way that will accept Chevy transmissions. (Yes, I had to get a car analogy in there.)
Electronics - Pickups have impedance. Not every pickup will work (well anyway) with the rest of the components in the system.
Then there is the issue of wiring in parallel, series, coil splitting, etc. It would be impossible (or at the very least impractical) for the rest of the chain to be wired in a way that all of these options would be available.
Also, I would argue that a solder (done by someone who knows that they are doing) is a MUCH better connection than ANY PLUG. The plug can come unplugged. It can get dirty causing a bad connection. It is just one more thing that can, and will, go wrong. (And, again, EVERY pickup company would have to adopt a standard plug, or at least make adapters, which would be ANOTHER thing that could go wrong).
Lest we forget that pickups are but ONE COMPONENT in your signal chain. So, if you are playing on your modular P pickup, and then you swap out to your modular mudbucker pickup, suddenly your amp is going to sound COMPLETELY different, both in tone and volume. I am also a sound guy. You would drive me NUTS if you did that all night. I am already chasing 47 pedals, 6 or more channels, various boosts, and various pickup selections and tuning with your two (or more) guitar players. That's all I need is one more fader to ride all night.
Plus, your AMP is part of the tone as well. Are you going to switch to a vintage Acoustic amp for your Jaco song, and then to an SVT for the next song, and maybe an 80's GK for an older RHCP song? That would be dumb too.
And in the studio, you have nothing but time. You can bring 50 basses with you and record every track on each bass if you like. So I don't see this as useful in the studio either.
"Douche move" - OK, recently there have been a string of "douche move" threads. Honestly, if I were at a show and saw some guy play "Mustang Sally", and then reach back on top of his amp and grab his "Zepplin" pickup and snap it in for one song, only to reach back and grab his "Ain't Too Proud to Beg" pickup for the next song, I would be laughing my %$$ off! Almost as much as I would if you brought FIVE basses to a live show. Guy, in a live mix, it really just doesn't make that much difference. You have dumped a metric TON of self importance on yourself if you think ANYONE cares that you didn't nail the mudbucker tone in that Cream song.
Short recap.
Marketing - There's no money in it or somebody would have done it. And all those manufacturers aren't going to cooperate to come up with a standard system.
Electronics - It is NOT as good as solder and is more likely to "go bad". It doesn't take into account the rest of the chain on your bass or the vast number of options people like you would want to have available from a wiring standpoint.
"Douche move" - Live, it's just plain silly to think that a sound guy wants to chase you all night or that the audience gives a crap whether or not you nail every tone. He doesn't and they don't.
(*sigh* Here's the part where I have to explain that this is just my opinion and that I don't hate anybody or think anybody is stupid. Unwad panties please. Here, I'll throw in some smiley face doohickies to help ease the tension







)