That _is_ a romanticized notion in our particular case. On his own, he quickly runs into obstacles, gets bored, and then fires up YouTube after about 5 minutes, in order to veg out.
I do teach him programming, though. He also does some more with his math tutor that comes in on weekends. He is kind of frustrated with our efforts at educating him. He thinks he should be writing grade-A 3D games right away, even though he utterly lacks both the programming and the math skills to do so. My advice to start with something much simpler has been falling on deaf ears so far.
Without structure, this particular 14 year old would not bathe, would not brush his teeth, would not do homework, would not properly eat, would not go outside or exercise, would not properly sleep, and would substitute all of the above with watching YouTube and playing Minecraft. So you can see why this is a concern.