Perhaps you meant instrumental rather than jazz or take a rather wide interpretation of what jazz is. (another debate altogether).

Thing is that, for quiet/fancy restaurants, the music needs to be somewhat in the background. Enough to distract away from random noises but not so loud that it drowns out conversation.

The thing about music is that we (humans) are quite attuned to the sound of voice. We tend to zero in on the vocal line and the instrumental accompaniment is less prominent (although it can be "jazzy") So loud vocals and accompaniment are unlikely to be played in a restaurant.

For instrumentals, the instrument (or instruments) has to carry that "main" melody but few instruments can replace a voice. So the instrumentalist will have to introduce harmonies and variations that hold attention without being "cheesy". Imagine someone playing the piano that exactly mimics a vocal line and it'll very quickly sound like children's nursery rhyme music (not what most people want to hear in a fancy restaurant).

So the instruments get to play a more prominent and varied role and that perhaps sounds "jazzy".