If you approach the question as a systems analyst would, you start with what the need is, and then progress to what acoustic characteristics will deliver to that need, and finally to designs, prices and brands that offer choices.
Jazz guitar can be played on any number of different designs of guitars. But because each design has its own acoustic identity, musicians tend to gravitate towards designs that work for the style of music they find themselves playing.
When jazz was developing as a genre in the early 20th century, the music paralleled the development of the guitar as a solo instrument. Unamplified, the instrument could not compete with the volume of the orchestra. The first stringed instrument that could compete, and the first to be identified with developing forms of jazz, was the tenor (4-string) banjo. This is a design with a floating bridge and a very loud soundboard - percussive (well, it is a drum head, isn't it?!) with a sound that could cut right through a loud ensemble. Violins share that ability to cut through the background - also using a floating bridge design, and a carved top as a transducer.
So the guitar developed into a carved design - arched top and back, having a percussive and powerful tone that could cut through the rest of the band. The attack and decay are both sharp; there is comparatively little sustain when plucked, and the volume is way, way up for an acoustic stringed instrument. Perfect for rhythm playing.
The guitar as a solo or lead instrument really developed with Charlie Christian and his work with Gibson - the first electric guitar was a carved top instrument with a magnetic pickup. And so it went. True archtops - carved tops and backs - are perhaps the most difficult stringed instrument to build, with the exception of the violin groups. That's one reason why they are expensive, and why most affordable archtops are pressed or laminated wood - not carved. An exception is the Tacoma archtop, a true acoustic carved top and back instrument which is available for under $2500. CNC routing is a marvelous thing.
You can learn more by looking at Linda Manzer's pages...
http://www.manzer.com/
I think you just turned a corner into a glimpse of Nirvana, myself.