Concidering a giant turtle taught Aang it's safe to say it wasn't avatar-exclusive, just it happened to be exclusive to the avatar. Just like how the avatar wasn't the only person who could communicate with the spirit world--Iroh was specificly mentioned as having a spirit journey--but it sure came a lot easier.
Remember in the story of Omashu that both Oma and Shu both learned earthbending from watching the badger moles. Likewise, firebenders worked out firebending from the dragons--apparently a trippy experience for them if Zuko is any indicator--and the push/pull of the tides taught waterbenders. Airbenders (somehow) figured out airbending by watching the sky bisons.
Actually, I'd like to complain about that.
- the things fly somehow, which airbenders had no idea how to do
- Sky bison, at best, twiddled their fingers and flapped their tails
- No part of the air bender mentality seems to, in any way, be based at all on the giant flying cows
Despite all that though they magically worked it out. That's (apparently) why they can make air wheels and have built-in climate control.
The concept behind energy or chibending is entirely of changing the base physical and mental core of a person. One could make the point that Amon isn't even chiblocking per-se but simply using acupressure to terminate the end of the flow of chi through the body, thereby preventing one from extending it beyond themselves third-eye-style in order to bend elements. If that were the case, with proper training one could remove the restriction.
Chibending would require not only you tamper with one's being but expose your own in order to do so. This was the reason for the struggle, and why the avatar spirit has a certain advantage at these things. Mere accupressure-based martial arts, of which traditional and modern chiblocking are a part, could never do this irrepairably or without side-effects. In particular, under traditional chinese medicine, (to plagarize wildly) physical dysfunctions of this chakra are brain tumors, strokes, blindness, deafness, seizures, panic, depression and confusion.
Please note how a certain pro bending champ suffered wild depression after having his ability stripped. Slow, semi-slurred speach, depressed attitude, sleeplessness, etc. Ozai didn't however, and was still rather fiesty for a crazy loon locked away in the depths of prison by his own throne-usurping son. He certainly was sharp as a tack.