I'm not sure you fully understand,
"For example, in the imaginary society, one might or might not be intelligent, rich, or born into a preferred class. Since one may occupy any position in the society once the veil is lifted, this theory encourages thinking about society
from the perspective of all members".
The bolded is the pertinent point in Rawls opinion in this state of nature we are concerned about society as a whole rather than an individualistic approach.
I think Hobbes social contract theory is more in-line to what your suggesting,
"In addition to Subjectivism, Hobbes also infers from his mechanistic theory of human nature that humans are necessarily and exclusively self-interested. All men pursue only what they perceive to be in their own individually considered best interests" [...]
This of course if you agree with the principles of social contract theory
Social Contract Theory*[Internet Encyclopedia of Philosophy]
Paul