Definition of Nucleophilicity
As far as I remember from my lectures nucleophilicity has the same definition problems as electronegativity.
So unlike e.g. ionisation energy you cannot define an absolute scale of ordering which you can verify experimentally
and just as in the case of electronegativity there are several possible definitions (compare https://en.wikipedia.org/wiki/Nucleophile).
Similar to electronegativity the definitions arrive on quite similar results. ($\ce{Br^-}$ is a good nucleophile in polar, protic solvents...)
Other formulations should be "qualitatively consistent" with previous ones.

Your alternative formulation has two big problems:


There is no solvent dependency.
You completely omit steric effects and nucleophilicity is also a kinetic phenomenon.