First of all it's not one edge.
Hero - 1 average edge, 21k commerce exp - 2 average edges, 10 retrievals - a bit less than average edge, 1 400 role exp - average edge, leadership - average edge, tattoo - a bit more than average edge, lastname - few edge points.

Warriors get few very useful edges as well as assassins. But there are much more good assassin edges than just few good edges for warriors.

So in the current system everything is alright.

But if we add few more edges for everybody because of obs/exploration exp then an assassins get much better edges than a warriors because of it's quality.

P.S. Overall i don't agree why some classes got much more love with the quality of edges than others. The system became less balanced than before. For example why do assassins need edges to improve martial trance or throw or vanish?!