I've struggled to teach this to jazz students, I know when I was a kid I read the same kind of advice in guitar magazines, and while I don't think that the theory-first advocates are malevolent, I think most of them were not serious jazz players and were getting paid to deliver a monthly column.

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.

As I alluded to in another comment, you are fighting upstream against the dominant Western conception of learning. But any musician I have ever met worth their salt knows the importance of learning songs and transcribing their favorite artists.

I think one of the causes is that some people struggle for years with music and then one day they learn a bit of theory and they experience a moment of enlightenment. Suddenly, all of their confusion is dispelled and what was once difficult is clear as day. They then think "if I had only know this years ago I wouldn't have struggled!". But they are wrong. It was the years of struggle that helped them understand the theory, not the other way around.

It's the "wax on, wax off" of Karate Kid and the wise old Mr. Miyagi.

I read a music theory book from the 1800s and in the first chapter the author stated that while he endeavored to write useful theory to help students they must realize that if some composition they write follows all of his rules but sounds bad, it is bad. And if they write a composition that breaks his rules but it sounds good then it is good. These are old, old ideas that we re-learn over and over.

Good analogy. There's a flip side to it though. You can be a great comedian on the level of individual jokes, or short bits, but be unable to write a story. And you can be a great jazz musician when it comes to soloing, but be unable to write a song. Stan Getz was a famous example. So yeah, learning jazz by imitation and immersion (as one learns a language) is very cool: learning these hundreds of songs will most certainly teach you how to solo. But it won't teach you how to make a song. Not nearly as reliably. It needs something else, I don't know what.