IMO:
A good chunk of it has to do with myth and legend (especially that Jamerson recorded all those Motown records with a B15).
The other reasons might be because of what might seem to be the many limitations of the amp that you list:
Very little headroom - It's just about right for a recording studio. You can actually turn it up and get that nice warm harmonically rich tone without pushing the volume too high. You can even push it just to the edge of distortion and the volume is manageable for a recording studio.
The speaker is narrow in its passband - It slots into a mix right where it should. It doesn't take up a bunch of sonic space that crowds out the other voices. Same reason a Pbass is so popular in the studio - it just works. Think of how many guys now have to have a HPF and LPF as part of their rigs. It used to be that the speaker could take care of those things for you.
Other than that, the amp - or I guess the preamp - by itself is just a very simple tone machine that works great for a bass guitar. It's a super simple tone stack that is flexible and just kind of sounds good. And good tone is not just limited to any particular genre.
As far as a modern gigging amp, they are not practical - mostly having to do with headroom / volume.
But, VERY cool in the right situation - IME.
If you are in a real recording studio (meaning proper isolation rooms), then it is perfect. On the right gig, in the right venue, it can be perfect.
In the studio:
View attachment 5297647
On the gig:
View attachment 5297648