I have to agree that the Jazz isn´t necessarily a bad pickup, even if not quite my cup of tea, but the name is a huge mistake.
In my years in retail I sold 2 jazz humbuckers. One was to a high profile local jazz player, and the other was for a Jackson that some Mustaine fan wanted Duncans in. Had it not been for mustaine, the number would have been zero, because tMustaine using it then was the only thing that convinced him. Without Mustaine he´d probably have opted for a Fullshred neck.
Unfortunately, the Jazz cat was far from pleased, "Wie ein Eispickel durch die Stirn" (eng. "Like an Icepick through the forehead"), and that made it almost impossible to get any non-rockers turned on to Duncans for a good 3-4 years, during this time all the Jazz and blues guys were buying up Bartolinis, Fenders, Häussels and Benedettos like hotcakes as a result because I also carried those and they´re tried and true. Interestingly enough Dimarghzio was never a real player in this area, or at least not one that I´d taken notice of...
As shallow as this may sound, just imagine if, say, Joe Pass were still alive, and wanted to switch out a pu for a Duncan, and chose the "Jazz" becasue he lileky wouldn´t be wanting to play death metal.... I can imagine that might still go sour pretty quick, because while cool enough output wise, it´s tonal response is more or less the exact opposite of what most people think of when they hear "jazz".