Using a pedal for this seems to me to be a largish hammer to crack a very modest nut. If I bring two basses, I adjust the volume control on the loudest one to match the maximum output of the quietest one, and adjust volume to taste on the amp. Job done.
That would almost work for me, but not for someone who constantly tweaks his/her volume knob during a show — with a huge disparity between, say, an active fretted and a passive fretless, our bass-brother/sister would still need something to even out the disparity beyond what the volume knobs on the individual instruments are capable of. Or as Garrett77 just pointed out, a fade out and I'm sure there are other reasons/situations; seems simple enough to return to the same spot on the pot, but in the heat of battle...
Stick a passive volume knob in a box (wait, hasn't EHX already done this?

), BUT with a two-channel (or more) switcher. The lower-level instrument goes in the channel without the pot, the hot-output instrument goes through the attenuator.
What works for you or me, doesn't necessarily work for other people's gear, playing style, situation.
On many active basses there is a trim pot on the pre-amp controlling the gain level from the pickups going into the pre. Besides that most basses do have a volume knob. I know not many people are aware but yes they do in fact exist on basses.
Not everyone is rocking an active bass. Also, MY bass does NOT have a volume knob on it, at all — it's one of those ones that's played vertically, not semi-horizontally. All controls affecting my bass are pedal-based.
And for all the thread-punters spouting "adjust at the amp" — I haven't had to/been able to bring an amp to a gig for several years now. I'm lucky if I get a backline amp, it's mostly been DI.
... I'm still curious about the actual initial question. Can we "level" output signals from varied input signals with pedalboard-friendly tech? It does sound like compression is one way to approach it, but I'd prefer just an output volume restrictor.
Does this exist? Do we have the science?
I think it could exist, but not enough demand for applying the science to the tech to warrant putting the money, time and effort into achieving the goal on a mass-production basis given the other solutions in the thread, considered band-aid ones or not. What is a compressor but an "output volume restrictor"?
A combination of the current tech would do it: your output volume restrictor (an EHX Signal Pad perhaps?), a comp/limiter, and instrument switching and maybe some of the other ideas in the thread — put them all in the same box, you could have as many inputs as needed, each with its own volume control (passive/active switchable), and all routed through the comp/limiter. Boutique build, sure, but it'd work and not have to conform to mass-production quirks, short-cuts and constraints.
A simple volume pedal could work, although you need a good way to adjust it during instrument switches, if you can’t play a few notes and do it by ear.
Visual Volume genesis:
I had a chance at a super-sale priced Visual Volume when I was first starting out. Didn't see the need for it on bass at the time, later regretted not getting it. Might mod my Dunlop DVP1XL...