To me, bass players get a chance to shine in genres that aren't currently considered mainstream - jazz, prog, fusion...these things were all popular many decades ago. Heck, even disco has some good bass guitar in it, with really great grooves and melodic bass parts. Once the 80's hit, popular music drifted towards punk, hair-metal rock, and early rap, all of which took the attention away from the musicianship of instrumentalists and gave it all to the visual and personal aspects of musicians/performers.
There was a resurgence of instrumentally-oriented rock music in the 90's and 00's, but nothing that, I think, really let the bassist of any band really shine. Unless you were a fan of the band, you probably didn't know anyone in it besides the lead vocalist and/or the guitarist(s). If you were lucky, the lead vocalist was ALSO the bassist, but those are rare cases these days.
I think the above analyses about where the attention lies is quite correct - the people up front, meaning the vocalist(s) and guitarist(s), get the most attention, in the studio mix and on stage. Drummers come next because, let's face it, people love drummers and love to air-drum and watch drummers play - there's a lot of movement and sound there. Keyboardists come next because their sounds are unlike guitarists, and often provide cool chords to back-up guitarists, or do crazy-sounding leads. After that, there's the bassist, who often acts as the guitarist's root notes/lower strings, and also the keyboard's left hand. If you're lucky, there might be an exposed bass solo during the bridge, or some crazy bass part there (like Cee Lo Green's "Fuck You", AWESOME bass part in the bridge).
It's sad that virtuoso bassists' only output can be bands that allow that sort of playing, like jazz and fusion, or prog and maybe some genres related to metal, where speed and technicality are important. Pop music often relies on synthesized bass notes, done on keyboards or other instruments, and with the recent advent of "dubstep", the bass sounds in songs have been relegated to womping-wubbing sounds. Bass, in popular music, has become something that is now only usually done to be felt rather than appreciated, which is why many people install huge bass speakers into their cars so everyone in the neighborhood can feel their bass.
For me, bass (be it guitar or string bass or any sort of bass-sounding instrument) is meant to be heard, not felt, but it's cool if you can do both and still be tasteful and creative. Rock bassists get forgotten and go under-appreciated, and it's a shame really.
-Marc.