It sounds a little like, reading the responses here, that the pickup comes out when the majority of responders have, for all intents and purposes, abandoned their expectation of getting a good acoustic sound
I think you are drawing a false conclusion here. I still tried for an authentic sound, and IMHO I was able to get closer using a pickup than a mic. The bleed from a mic tends to pick up a lot of sound from the room. If you send the mic through an amp, a feedback loop is formed and the sound is amplified over and over...and it no longer sounds like the bass.
Having a feedback loop does not necessarily mean you have squeals and squawks of feedback. At lower volume levels the feedback just makes the sound more diffuse and less coherent. By the time the sound travels electrically to your amp and speaker, and then acoustically back to your bass and mic, there is quite a bit of delay. This means the amplified sound arrives back out at the mic delayed and out of phase, so the impulse and frequency response is distorted. Keep in mind the feedback loop is continuously in action, so it can hold remnants of sound you played a second or too early...this has the effect of smearing out detail.
Bleed from other instruments was also a significant factor. In our experiments the cymbals were significantly louder in the mic signal than the bass. The person who bought the mic (AMT S25) tried turning down the treble on the mic to compensate...but IMHO this degraded the sound of the bass so much that it made using the mic pointless. He also tried blending the mic with a pickup. If he turned up the mic to the point where it could be heard, it tended to make the sound worse, rather than better. There was only a very small window in the volume levels between when the mic could be heard and when the feedback loop became so strong that it rang continuously.
The main advantage of a pickup is it focuses more on the bass and less on the room and other sound sources. This gives you more gain before feedback. It does not eliminate the feedback loop, but it's pushed down significantly further in the signal, unless you are playing very loud. As you turn up the volume, the feedback loop grows stronger and stronger...so you get sonic degradation with a pickup as well, but this degradation comes on much slower, so you have a wide range of usable volume you can play at.
To some degree you can correct for some elements of the degradation produced by the feedback loop by using mirror image equalization. Consider the bass, pickup, amp, speaker, and room to be a system. This system will have resonances that become more active as the gain is turned up. In other words they will produce peaks in the frequency response that distort your tone. As you turn up, these resonant peaks tend to grow bigger. With mirror image EQ, the idea is to try and add dips to the system response that is exactly the opposite of the peaks produce by the resonances. So as you turn up, you need to increase the depth of the dips to compensate.
In a controlled environment where their is no feedback loop and the room has good acoustics, obviously a mic will sound way more natural with way less effort. As soon as you introduce a feedback loop, the sound is rapidly degraded with a mic and no longer sounds natural. A pickup is way less sensitive to degradation caused by the feedback loop.