Boy have things changed. Try finding any significantly popular newer musician doing anything like this these days. Even the soul music revival of Amy Winehouse and friends is gone now. Everything is either very folksy, or very very minimalist and/or electronic. Singing is very loud, or angular, or folksy, but jazzy... not very much. Hip hop is about as un-jazzy these days since it the electro craze of the early 80's.
These things come and go, of course. Rock'n'roll had roots in the jazzy sounds of rhythm & blues, but very quickly developed its own less jazzy sound. As the late 60's approached, musicians were eager to explore newer sounds, and started incorporating those jazzy elements back in. Much of the popular music from the 1970's had jazzy elements, and continued to do so until the new wave era brought a whole new sound to popular music. Electronic instruments became affordable, and soon everyone want to create a more robotic, digital sound to their recordings. The 80's might stand as the least jazzy era for all of American popular music.
But, of course, that rigid 80's sound could only last so long. Digital samplers actually helped change this, allowing hip hop artists to easily sample old jazz and funk recordings, creating a more retro-sounding hip hop that was all the rage from the late 80's through the late 90's. Many techno artists did the same, creating new genres of dance music that were far more jazzy and organic sounding than anything the original techno artists had originally envisioned. Indie artists started to jump on the bandwagon as well. Some (such as Beck), being heavily influenced by the new hip hop music. Others, such as Stereolab and Yo La Tengo, being influenced by more arcane styles of bygone eras. But it wasn't just the artsy-indie crowd who was doing this. Punk rockers also started to incorporate jazzier elements as well, particularly those in the ska/swing-revival scene. And of course, adult contemporary artists were becoming more and more jazz influenced as well, particularly encouraged by the popularity of artists such as Harry Connick Jr and Norah Jones. By the late 90's and early 00's, it seemed as if just about everyone outside the world of the heavy metal and industrial rock were expected produce at least some kind of music with jazz elements.
But nothing lasts forever. What once was new and novel begins to seem like boring and unoriginal. By the 2000's the new thing (if you really wanted to stand out) was to revival the old angular, jerky sounds of post-punk and new wave music. Hip hop and dance artists looked back to the older electro era for inspiration again once more. Everything 80's was suddenly trendy again, and jazz revivalism was just no longer interesting to almost anyone. As the post-punk revival faded, a new folk-revival took its place. And from that came newer indie artists blending a variety of different styles together. The inspiration came from numerous sources, but one thing they all had in common was an avoidance of stereotypical jazz elements. You were far far far more likely to see a banjo and accordian in this new indie music than the vibraphones, trumpets and other jazzier instruments the previous indie artists were exploring.
So what happens from here? I doubt jazz influences are gone from popular music for good. Within 10 years it'll probably become trendy for some movement again. But by that point in time other genres will be old enough to seem cool and interesting again. The question remains: by the time the current fads have died out, will I be able to enjoy whatever comes next? Or am I a cranky old man forever? :-D