I started playing regularly and seriously only last year and I played an already fairly modern passive P+J bass (budget brand, early noughties), so I don't have experience with older guitars.
I think these two statements are true:
• Fully passive instruments have comparably low outputs (though significantly higher than they used to have half a century ago). So putting a phantom or battery-powered preamp in the guitar itself makes perfect sense. The signal is hotter, it has more headroom, interference induced noise has less effect on the signal.
• Bass amps used to have two inputs, one for passive instruments, and the other for active ones. The active input simply padded the signal before the onboard preamp. You could achieve the same result by plugging your active instrument in the passive input and turning down gain. The only time when you needed to use the active input was if your bass runs so hot that it overdrives the preamp even with the gain turned way down.
So far, so good. But I bought an active guitar last year and I was surprised by one thing: the volume in passive and active modes is exactly the same. I read that this is common with all modern active guitars. I can tell for a fact that the preamp is in use because active mode won't work if the battery is close to being dead, and tone controls only work in active mode. When tone controls are in the center position, it's impossible to hear the difference between active and passive mode.
Active signal is not hotter than passive. It's possible that the noise floor is lower and you get higher SNR in active mode, but interference induced noise is additive. It doesn't care how much (or how little) noise there was previously. If there's enough interference, it will cause noise.
What gives? The only two advantages I see running the bass in active mode is 1) tone control; 2) impedance matching with badly designed amp input stages. Theoretically, there might be a third advantage that when used in a noise-controlled studio, your bass will have a slightly lower noise floor, but I'm grasping for straws.
What am I missing?
Your first two statements are not correct or should I say not entirely correct. Active basses usually have a hotter signal because there is a battery in the bass powering the preamp in the active bass. That preamp in the bass is what allows you to boost the treble or bass or the mids if it has a mids control. With a passive bass, such as my 1982 Jazz, there it no boosting or bass or treble. It has two pickups, one in the neck position and another one near the bridge. It also has a single tone control. All of those controls are "cut only" controls. To get everything out of those pickups, both volume controls AND the tone control needs to be turned all the way up. From that point any adjustment you make lowers the signal that goes to the amp.
Normally a passive bass does not have as hot of a signal as an active bass. But since passive basses have been around since 1951 and are still being made today, and since amp inputs are primarily set up to accommodate passive basses, it's not that the passive basses have a weak signal, it is that Active basses can have a hot signal, especially when you start getting into 18-volt onboard bass preamps.
Old amps did not have two inputs so you could use one for active and one for passive. My 1966 Fender Bassman amp that I bought in 1966 actually had 4 inputs - 2 inputs in the bass channel and 2 more inputs in the normal channel. Both channels had volume, treble, and bass controls in that order. The "bass" channel was too woolly and boomy for me so I always plugged my 1965 Jazz Bass into the "normal" channel. That was to allow two instruments to be plugged in or an instrument and a microphone.
The "old amps in the 60's and most in the 70's didn't have an accommodation for active basses because active basses, outside of Jack Cassidy's 1972 Alembic, didn't even make an appearance until 1974 with the first Stingray bass and didn't become wide-spread until the mid 80's. The whole reason I have my '82 Jazz now is because a guy traded it in at a music store where I was working, towards an Aria Pro II with active electronics in 1985. It was a bit of the rage back then although that was well before Fender made any active Jazz Basses.
There have been two different schemes for amps to accommodate active basses. One way that they were done, and still are done, is as you suggested with separate passive and active inputs. The other way you'll find more commonly is with a single input and a pad button or switch that will typically drop the sensitivity of the input by 10db to 12db or so. The problem with putting an active bass into a normal input is that when you go to adjust the gain, there is very little granularity to your adjustment options because it clips the gain section at a low setting, often around 8 or 9 o'clock. By pushing in the pad button or using the active input if it has one, the signal is reduced enough that you can typically set the gain somewhere between about 11 o'clock and 2 o'clock giving you much finer control over the strength of the signal you are actually sending to the power section to amplify.
I also have an active/passive 5-string bass. It's an inexpensive bass ($219 in 2009 when I bought it) and the active preamp is OK, but nothing to really write home about. When it is in active mode you can cut or boost both the bass and treble controls on the bass. When switched to passive mode, the bass and treble controls don't work, but the volume and the pickup blend knobs do work just fine. My Rogue 5-string has two pickups so the blend is quite effective in changing the sound. I play it almost exclusively in passive mode because I can get a good sound out of it by moving the blend knob just a little bit towards the bridge pickup in passive mode.
A big plus with that is that I don't have to change the gain setting on my amp when I change basses. I set the gain on my amp up for my Jazz. That setting is "close enough" for my 5-string in passive mode, that I can easily change from my Jazz to my 5-string and back again without touching my amp. In active mode, I have to either push in the pad button or plug into the "active" input,(depending on the amp) and then reset the gain. Plus, with the two pickups in passive mode, if I need a little deeper warmer sound I'll pluck the strings closer to the neck. If I need a brighter sound I'll play a little farther back towards the bridge pickup. A change of my plucking position by just an inch in either direction will make a noticeable difference in the sound. So if I don't want to mess with the blend adjustment if it's not quite right, I can just move my plucking position a bit.
i don't believe your bit about the noise floor is correct. The whole thing about getting a high signal to noise ratio with a low THD (total harmonic distortion) is to get a strong but clear signal out of the gain. My Eden and DNA amps all have gain set lights on them. To get the cleanest, clearest, and strongest signal from their gain section, I want that light to blink at my loudest and lowest notes. That gives me the highest SN ratio, the lowest THD, and the strongest signal for the power section to amplify.
If I have set the gain too low, I have to turn the master up to get to the same output level I can get at a lower master setting with the gain adjusted correctly. Problem with that is the SN ratio, which directly affects your noise floor. When you have to crank up the power section because you have the gain set too low, you send a weak signal to the power section. You turn up your master to get the level you desire and your SN ratio goes down AND you are far more likely to have additional noise from the power section as it works harder to amplify the weaker signal. That results in a higher noise floor not a lower one.
When you run an input signal through active electronics and then through the gain section of an amplifier you take a chance on getting more noise in the final output because it's going through two preamps - one in the bass and one in the amp. Gain settings become critical in that occasion. We are actually pretty long past having inherently noisy active preamps in basses, but we're not beyond the challenges in getting the "perfect" gain setting for our basses and sending too hot of a signal to an amp exacerbates the challenge.
I would agree with you that the active basses offer you more varied EQ choices and possibly better sound than a passive bass. Nonetheless, my 1982 passive Jazz Bass through my Eden and DNA gear is the best sounding bass I've ever played or heard. In a 3hr. recording session at a pro-studio in Seattle back in 2019, I was asked to go direct to the board with my bass because of bleed-over concerns with the bass and drums. So I pulled out my Eden WTDI, which is a DI box with built-in Eden WT preamp and plugged that into their wall connection.
I set it to the same settings I use on my Eden amps and at the end of the session both the sound engineer and the owner of the studio came out of the control room to see what the heck I was using. I showed it to them and told them I only boosted the low mids to 1:30 at 500Hz, running every thing else flat, and they were amazed. They said it was an amazing bass sound. The engineer said the only thing he did to my signal was adjust the level - he didn't touch the EQ or add compression to my tracks. I listened to it with his headphones in one of the isolation rooms and it was the best my bass has ever sounded. At the mixdown later, I'm sure he did use compression in places, as you do when trying to balance everything to get the best recording. But on the raw tracks, it sounded freaking great!