The analogy I've tried to use in teaching is that learning to play jazz is like being a comedian; when your skills are at their peak you're going to be inventing jokes regularly, but in the decades before you get there, you're going to be delivering other people's jokes putting a little of your own spin on them. The delivery matters a lot, and like good jazz playing it's pretty much impossible to write a book called "How to be Funny" that wouldn't just be an academic analysis rather than an instructional guide.
I struggled with jazz for the reasons I've alluded to above, and it wasn't until I started studying with a teacher who just had me memorize hundreds of standards that I got my playing together. We definitely talked about the technical bits of what was happening in the tunes, but those were really just interesting observations; repeatedly playing them in a group setting after woodshedding them at home between lessons, then taking a lot of solos was really what made it happen.
It really makes me happy to see up-and-coming killer players like Patrick Bartley espousing this same approach. Yeah it means you're going to spend thousands of hours memorizing tunes, but if that's not fun then playing jazz isn't going to be fun either.