It seems to me that you are presuming that playing a line of arpeggios and licks that fit the changes is improvisation and the essence of jazz. Well that opens up the entire question of what is improvisation and what is jazz.... You don't want to go there.... I have no idea how advanced a player you are, yet we can all put ourselves in the position of being in an audience. How much of your time and $$ will be spent going to listen to players who may be very well educated yet all they want to do is TAKE approval from you for showing off their technical abilities? How about instead, going to see someone who is in the entertainment business who knows how to GIVE and audience an experience? Having seen many of the "greats" in the 1960s I can verify that they GAVE performances to their audiences and most were not just technicians copying what players form 50 years before their time were playing. Being aware of a melodic line can be very important. Some of the best improvisations (the sort you may be most familiar with) are melodic variations. These have the ability to restate the melodic line in a personal way which is integral to that musician. It's when the audience feels that the musician is saying something very personal, just to them...special. As a player you need to know music and your instrument...that's obvious. As an improviser you can do the cut and paste and possibly even do this very well as a technician, yet does it say anything other than "I'm playing notes that fit within the changes"? Do you get this distinction? One is improvisation based on playing what you hear internally and GIVE to your audience. The other is based on finger memory (and a lot of very hard practice), but at best a technical exposition without an artistic or personal point of view. Its intent is to impress and TAKE approval from an audience. A name for this would be "stillborn improvisation". Yes, there is a very distinctive divide, and every audience knows it and can feel it.This is a terrific discussion thread, but the either / or debate doesn't ring true… isn't the basic improvisational craft about doing enough practice that the chord-scales become second nature so that harmonically you can stay with the tune you are trying to improvise over… and then its all about having a good tone, sense of rhythm, and just being good enough (lived enough?) to introduce all the other variations to put some "life" into the improvisation; but getting too free for most of us can just mean you can't hang it on the melody and chord changes? I heard a great quote in one of the old videos I had (I think it was Phil Woods talking about Cannonball - but my memory fails me), saying he asked him if he could use a lick and Cannonball was like… "did I play that!" but also said "if you can hear it, you can have it".
Learning to play mechanically without reference to your inner voice (IMHO) is not good training. This is now recognized in much of the CLASSICAL world with methods like "Suzuki" being about ear training and making you one with your instrument. Those trained this way, if they have talent, can play what they hear, without reading music, whether copying, or improvising. It's also increasingly being recognized in the teaching of many other instruments and styles. For some reason the sax seems to be a bit retarded in this respect, and it's a shame as the instrument continues to dig a hole in which it buries itself with the public's cliched view typified by the Simpsons or Sesame Street. As mainstream style jazz continues its decline will the sax follow it into oblivion? Here's a reminder: The clarinet used to be a very important instrument in popular music. It unfortunately got itself tied to Dixieland and Benny Goodman style music. The result is obvious. The sax is one of the most versatile instruments available and the one most like the human voice. Staying in the same place by perpetuating the same style of playing makes you a museum piece. Music and the arts move on. There will be a few jobs for mainstream style players...very few, like Dixieland.
The article that started this all off seemed (to me) to recognize this and encourage players to learn their craft and then develop their own voice. A very long curriculum that gives emphasis to copying and does not encourage development of one's unique voice could doom an otherwise talented musician to oblivion. It's been said, and possibly needs repeating, that it's not possible to name a famous artist or musician who studied and got a PhD. Did none of those people have talent, or did their talent become subsumed? Paint by the numbers is the best method for an untalented person to paint any picture. Likewise it seems that the culture of copying and using cut and paste style technical improvisation is another "paint by the numbers" or "anybody can play music" type of exercise. It's not necessary to put anyone down for doing what they can and enjoying painting or playing. Where the cut lies is with those who have talent and are being trained with the same "paint by the numbers" style. We need talented players, and the instrument needs to move forward, not forgetting the past, and not without learning basics...yet certainly not continually wallowing in the past and continuing with a system of teaching that has failed so many.