• Is this compiled half-knowledge correct?
Yes, it is correct. Correct enough anyway.
• Why is such a circuit rather uncommon - or if it is more common, where can you find it, and if not, why does it make no sense?
Actually, these types of circuits are not uncommon. The Stellar Tonestyler is a commercial example, although it does not simulate different resistance values - only capacitance, AFAIK. There's a schematic DIY version floating around here on Talkbass someplace that does include additional resistors. I'll leave that search up to you.
I once built my own DIY Tonestyler and added it to one of my basses. In a real-world working environment, I did not find the feature to be very useful. Just having one set capacitor wired to a pot is far less awkward to adjust and dial in. It might have been a little more useful to wire the varitone to a pot in order to vary the degree to which the capacitor sends high end to ground. I'd say for you, that experiment might be worth a try. For me, it wasn't worth it enough to have more than two knobs on my control interface.
• What values would you set for the resistors, capacitors, and the resistance of the pickup?
As far as caps, a stock Fender cap is 0.047uf. Say you had 10 settings on a switch. You could make 0 your open setting, no cap. 5 your 0.047uf setting. Maybe 10 as your .1uf setting. Everything else you could set as increments in between. Every increment should be double the last. Personally, I found the mid-bump with the smaller value caps to be the most interesting. My prediction is once you get past 0.047uf, you'll find that you'll just have more bass.
As far as resistance, if your pickup is say, 7K, you'll find that once you get past a pot value of 500K, you're not going to hear much difference. The lower values have more effect on the sound of the pickup. I'm the last person in the universe qualified to quote anything even remotely related to electrical engineering, but just in case you want to know, it works something like this: Between a pickup (R1) and a pot (R2), you're wiring two resistors in series, so the the formula will be RT = 1/(1/R1 + 1/R2), with RT being resistance total. In this case, a 500K pot will give you 6.9K total and a 250K pot would give you 6.8K. 0.1K doesn't seem like a heckuva difference, but the pickup with the higher value pot will sound noticeably brighter.
Pickups wired straight to the jack can be pretty piercing - that's kind of the rational behind tempering the high end by using a pot.
• What disadvantages might arise from such an approach?
If you have the time on your hands to do an experiment like this, then I don't see any disadvantages.