All pickups I've used sound better through an amp than when recorded direct. My take is when going through an amp you are hearing the room along with the processed sound from the amp. When recorded direct, those effects are missing and the dry sound of the pickup alone is quite often more "boxy" sounding and less natural, without the elements that contribute to an acoustic sound.
A recorded pickup sound is useful for mixing with good mic sound to give "center" when needed, particularly with drums.
I don't disagree with this, but if people refuse to EQ the direct pickup sound, it's not really a fair comparison. Comparing an unequalized pickup to an unequalized mic should always favor the mic, unless there is excessive bleed from surrounding instruments.
The bass does not really have much impact on the response of a mic. You do have to deal with proximity effect and how narrowly the mic focuses in on a specif part of the bass. These thing are dealt with through mic technique (aiming and distance) and possibly a bit of low frequency EQ and/or application of an HPF.
Since the pickup is fixed to the bass, the resonant qualities of the bass have a significant impact on the frequency response of the pickup, which varies depending on the qualities of the instrument and where/how the pickup is attached. The pickup and bass essentially form a system.
If you really want to compare the sound of this system to the sound of the bass mic'ed, you have to make some effort to EQ the system so the frequency response is comparable to the sound you get with the mic. AFAIK, this is what the ToneDexter attempts to do.
Also as you have correctly observed, the pickup does not sense room reflections. Depending on the polar pattern of the mic and mic technique, a mic may not sense a significant amount of room reflections either. But usually when recording, the mic is far enough away that you at least get a little sense of space. This may not be true if a mic is used for sound reinforcement.
This sense of space is something that can be created around the pickup as well with the proper digital effects. But in a mix, it's often desirable to have the bass dry unless the mix is very sparse. So although the space in the mic'ed recording may sound nice, it's not always beneficial.
Actually some pickups tend to exaggerate vibrations of the bass's body, and I suspect some of this is related to sound reflections within the bass. These vibrations can be put back in proper context to some degree by dipping the associated frequency range with parametric EQ.
For example, hen I first listened to the EAP in the video I linked in post #21, it sounded horrible compared to most of the mics. The reason is, because I was listening on a laptop that has a boost at 125hz and 250hz. When I put on my headphones and disabled the boost, I thought the EAP compared much better to the mics, but there is still some extra emphasis between 125-250hz that makes it sound a little boxy.
IMHO this sort of non-linearity in the combined response of the bass and pickup should really be addressed before you compare the sound to the mic'ed bass. Don't simply throw up a mic, mount a pickup, and hit record. Find the optimum placement for the mic and pickup, and tailor the EQ for best sound. IMHO that's how you do a fair comparison.
The idea of comparing them without equalization has no efficacy, especially since many pickups verge on being unusable without massive amounts of corrective EQ.
The reasons you point out for why a pickup sounds acceptable through an amp are valid. But part of the reason the pickup sounds acceptable is likely because you twist the tone control knobs on your amp. Also the amp and speaker may be voiced instead of full-range-flat-response. In other words the amp and speaker essentially may have baked in EQ that helps the pickup sound better.
I still think a mic is going to win for capturing the most authentic sound in all situations where bleed from other instruments is not a concern. But a pickup can sound surprisingly good. The ability to make a pickup sound as mic-like as possible is a great skill to have when the bass is used in higher SPL situations where a mic simply won't work.
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