My guess is that the profession would become a lot more attractive to the average kid that is very smart, but doesn't have an interest in law or medicine. Other guesses are that security would become absurdly good in general, and a lot of tools would be perfected.
Instead, the importance is placed on loving programming, because you're going to have to love figuring out what you need to be educated in and love providing for that education out of pocket, and with no credentials to show for it. So you're on an equal playing field with anybody off the street when dealing with an HR department, and at a disadvantage against a CS graduate who may not be able to program to save his/her life if you didn't go to school to learn the math, but simply learned your profession.
To have a capital-p Programming educational track like Law or Medicine could really be a boon for the profession in most ways in my opinion. Could somebody tell me where the Perl class is? Because I can't seem to find it or get student loans to cover it.
The one thing that I think would be problematic would be an injury to Free/Open Source software, because practitioners wouldn't feel the necessity to put that evidence out there that they actually can program, like surgeons don't feel like they have to stream over the web live operations they are doing for free.