Is rating a fighter on the basis of social importance relevant?

I think it can have its place, though when I make my own lists up, I do not let it be a factor.

I think you can make some kind of master list, where you combine overall skill, quality of opposition, wins, performances, legacy, social impact, etc all into one. But, but it would be tough to place weight on one thing or another.

It says a lot for a fighter to define his era, usually, fighters who do this must have more than a few reasons why they do that. Joe Louis wouldn't have been a national hero if the people who saw him didn't think he could fight well.
Ditto everyone else.

Depends on how you look at things.