I think the "modern" bass sound was birthed with the Music Man Stingray, but it was a long gestation. There are plenty of "vintage sounding" records that used pre-EB Stingrays: Rick James -"Superfreak," most of Stevie Wonder's 70's catalog, etc. When pop music became dominated by keyboard bass in the early 80's, pop bassists began dialing in a lot more upper mids and highs to create bass sounds not easily duplicated by the synths of the day and the most accessible active bass at that time was the Stingray, so a Stingray with dimed highs became the norm.
Also around that time, bassists like Jaco and Stanley Clark began to play the bass as a harmonically lead instrument making round low mids and lows less important than a strong upper-midrange voice. Add Flea's slap funk and RHCP's mega popularity to the mix and music-fan kids came to accept the idea of bass being front and center. As bass playing became more populist and not just the red-headed stepchild refuge of failed guitar players, lots of people began gravitating to more "modern" voiced instruments and amps, and like a lot of things in the 80's, it was well overdone. In general, I find that beginning players like modern voicings and as they "mature" as players, they move more towards "older" sounds.
...of course, this doesn't even begin to address amplification, which figures in very strongly in its own right.
