Two Reasons that I'd suggest:
Location, Context, Cost: Where are church organs? In churches... jazz is commonly a rejected genre preference by churches that own church organs. Remember that is today, just ponder on the rejection jazz would of received from churches in the era in which jazz originated. Clearly the church organ wasn't off to a good start in the culture of jazz. Many of the instruments in main stream jazz aren't that all expensive in the time of early jazz and back then it was a source of income for many families. So there would always be a neighbour or household in the street with a piano or other affordable instruments (guitar and woodwinds). Many of the homes would contain mini church organs too, but who wants to lunk that thing around gig to gig when you're trying to make an income?
Sound: Just like any genre, the culture of a jazz defined its basic 'what's allowed' instruments many years ago, most of us still stick to today. In fact, Google's definition of jazz literally contains those main stream instruments that were defined in its making. You'll notice that all the instruments that are mentioned all share a common theme, they're mellow instruments or can be played that way. Since the church organ is reliant on great amounts of air pressure, being mellow is simply not an option. The church organ would simply overpower a jazz band. Therefore, a church organ would simply throw off main stream jazz.
Overall, the reason why the church organ isn't commonly seen in jazz is because the instrument was impractical in era in which jazz was defined. Think of rock'n'roll, it was defined by electric guitars, drums and some crazy singing, why don't we add bag-pipes to rock'n'roll? The same goes with church organs and jazz, mainstream musical culture. However, as technology progressed having a church organ can now be as accessible as clicking a button on your keyboard. Since that, the organ occasionally makes an appearance in jazz, usually with the rotary effect. See! But still not that common because of the genre's culture.