John, I think you make a valid point. I remember one day a couple of months ago when I had an hour to kill before driving to a rehearsal, so I did my best to dial in, EQ-wise, four separate signal sources:
1. A Ric with a nonstandard wiring scheme,
2. An '80s Charvel/Jackson P/J with just the P pickup enabled,
3. Same with just the J pickup enabled,
4. Same with both pickups enabled.
The Charvel/Jackson had active EQ but I left the tone controls centered.
I have to say, I got all four pretty close to one another using just the controls on the amp(s), and certainly close enough that no one would ever notice in a live setting.
The extremes were #2 and #3, requiring the most dialing-in. #1 and #4 required far less, and more or less defined the middle.
This was limited, however, to traditional two-finger playing. No slap, no pick. Those styles might've brought in different results.
Bring in an EB0, though, or one of those '70s Telecaster basses with the big shiny pickup up near the neck, and all bets could be off. And a Telecaster player could rightfully say all bets would be off if he were to bring in a Music Man with a single pickup down near the bridge and, using only the amp's controls, try to get it to come close to the Telecaster. I think sometimes there's just too much distance between two specific instruments and it can't be bridged by any amp's controls.