The avatar world seems to adhere to a pantheistic spirituality. This fact is alluded to in the swamp and the guru episodes of ATLA and using this fact to shape how we view bending can clarify several things about both the avatar and Amon. There are four nations and four elements but in the grand scheme of things they are all part of one spiritual whole, they may be physically separate but they make up the singular entity that is the world of Avatar. The four nations represent four different cultures, geographical locations, and societies which together make up the world. The avatar then is the manifestation of this whole, the spirit of the physical world, so it makes sense that they would possess all four bending arts.
The four bending arts are also connected in the sense that they are methods of manipulating energy (kinetic for earth, water, and air, heat and electricity for fire, vibrational energy for seismic sense). A pantheistic worldview allows for humans to manipulate the inorganic material of the earth because they are all part of the same spiritual whole, so bending is both a physical and spiritual process. The dualistic interaction between the physical and the spiritual is representative of the avatar's role as the bridge between the physical world and the spirit world which lends credence to the avatar being the ultimate bender, they are the physical manifestation of what bending is. It seems to me that energybending is not a method of manipulating physical energy, but a way to control spiritual energy, to impart knowledge or alter how an individual spiritually interacts with physical energy. Energybending allows one to block the access of a bender to the spiritual energy that lets them bend, but does not allow nonbenders to become benders because there is also a genetic component of bending, once again, an interaction between physical and spiritual elements. It is possible that the spiritual connection that allows for airbending is not present in Korra until she "unlocks" her airbending by connecting with the spiritual energy that allows one to airbend. Why she unlocked her airbending when she did is unclear but it is likely that the massive spiritual and physical disruption of having her connection to three elements severed triggered a heightened physical, mental, emotional, and spiritual state that allowed her to unlock airbending, perhaps with the aid of the knowledge of her past lives delivered to her by her connection to the spirit world.
This then leads to the more difficult question of how Amon removes bending. If the process that he uses to remove bending is a wholly physical event, why would the manipulation of spiritual energy restore bending? We can resolve this through the fact that religious experiences have a physical manifestation, primarily in the prefrontal cortex of the brain in our universe. Amon's hand position, one on the back of the neck (presumably manipulating a pressure point to subdue the victim) and one on the forehead (to manipulate frontal lobe brain activity) fits into this theory well. It's all a bit speculative and nebulous, but perhaps Amon is able to change brain activity through some alteration of blood vessels, neurons, glial cells, or brain fluid to prevent spiritual activity in the brain. This would be an extremely difficult and precise usage of bloodbending, but it would explain why healing is not effective in restoring bending. Amon would first have to use a heightened knowledge of the human body rendered to him by bloodbending to discover the part of the brain that saw increased activity during bending, presumably a part of the brain that deals with spiritual experience. Amon was unable to detect the part of Korra's brain that deals with the spirtual experience of airbending because it was dormant until she unlocked her airbending. Healing would be treating the physical side of a spiritual ailment and most neural injuries are permanent. Amon's victims showed no physical side effects to indicate chi blockage, perhaps the effect is on a very specific region of the brain that interferes solely with religious experience. Only a being with unique spiritual talents (such as the avatar) would have the ability to detect and treat the source of the problem.
Amon's deceitful and nefarious manipulation of the interaction between the physical and the spiritual represents falsehood and illusion, just as Amon's character is a falsehood, a means to an end. The avatar uses energybending which requires truth and purity of heart and mind, piercing illusion with the light of spiritual truth. This contrast between Amon's deceitfulness and the Avatar's genuineness is reminiscent of platonic ideas about the illusion of the physical world and the true forms of a higher plane of existence. The avatar, a being that exists in both the physical and spiritual world, can shine a metaphorical "light" through the darkness of the falsehoods that exist in the physical world. Aang's quest was not only to defeat the fire nation, but to remind the world that war was not its natural state. The idea that the four nations should be in conflict was a deception propagated by the fire nation, Aang, particularly in season three, had to work to disprove this lie to bring the four nations back into balance. Zuko reflects on the power of this lie in "The Eclipse" and in season three we see that many fire nation citizens are good people who are caught up in a conflict they do not understand. Just as many fire nation citizens are deceived into fighting the other nations, the equalists have been deceived by Amon into believing that they can only achieve equality through violence.
Regardless of the nobility of Amon's goals, his entire life was based on lies and deceit and his movement was no exception. Amon has always reminded me of communist leaders, an uncompromising, charismatic, powerful leader who appeals to the interests of the oppressed. He is more Stalin and Mao than Marx however, his desire for equality ties directly into his insatiable ambition. His desire to defeat the avatar was not based entirely on an altruistic desire for equality, the scene in which he bitterly reflects to Yakone and Tarrlock that the avatar's ability to energybend is more powerful than bloodbending, the ultimate waterbending technique, reveals his formidable desire for power. Balance could only be restored to the world when Amon was defeated and those deceptions were disproven.
At first glance, however, it seems as though Amon's movement will bring balance to the world by "equalizing" benders and nonbenders, however, we must remember the dualistic nature of the avatar world. Bending is a way for physical beings to interact with the spiritual energy of the world. It is representative of the spiritual heritage of the four nations and of the world itself in the form of the avatar. Amon's movement may have brought socioeconomic balance to Republic city, but it would devastate the spiritual balance of the world. I hope that now that the issue of bender-nonbender inequality has been raised it will be dealt with further in the second season. I would love to see a character that counters Amon's violent revolution with a peaceful one. We saw the beginning of social change in "Skeletons in the Closet" with the equality between benders and nonbenders in Gommu's hideout, hopefully we will see a continued implementation of equality in season two.