Scruffy:

As for being a senator and having "soft skills," I think you overestimate the skill overlap, and make assumptions about the skills late Imperial Senators actually had. Leia's only apparent qualification to sit in the Senate is her royal station. Given the rather swift dissolution of the Senate, it seems none of the other senators brought anything especially vital to the Empire, either. Even if there is a significant overlap of skills, having the skills to be a diplomat does not make one a diplomat.

Who out of the Big 3 will do diplomacy? The naive farmboy, the blue collar Han or Leia when it's necessary? Discovering new cells, involving different rebel groups and managing their relationships is very important for the Rebeelion.