Well someone mentioned the themes
The Byakugan is the theme of insight
The Sharingan has themes of darkness and power
The Rinnegan has the themes of life and death. Death exhibited by the Asura Path: all the weapons symbolizing the destructive power of war, the Naraka and Human paths associate with death of an individual and the underworld
Life associated with the animals of the Animal Path, Life forces of mature represented by Deva paths control basically of gravitational forces. The Preta Path's taking in of chakra somewhat reflects how nature is all the same despite its various forms (different elemental techs).
I agree that the techs aren't exactly revolving around the eyes (the only ones close to it are the Preta and Deva paths), but when you think about it the abilities all come from the eyes lol!