Oh, please no
The league thing we have now is enough, we don't need another completion between team members. Maybe for a big FA FS like yours it would be fun but I doubt that would be the case for the rest. For most FS FA it's sort of a team building moment and that could have the opposite effect. Plus as Julian said not all badges are worth the same. I'll take 50 residues (or even 50 hats) over 50 blacksmiths or statues any day.
I fail to see anything in common between the 2? The league is not much of a competion at all (unless you call money spending a competition), and the little there is, happens between players on the entire server not within a FS?
But I can see that you might have a negative effect in a FS, if you have people that don´t contribute much (for whatever reason) at all. Either them feeling bad or more competitive FS members behaving badly towards them. But that to me sounds like there are pre-existing conditions in such a FS, that better get sorted out regardless of any FA...
I mean we do exactly the same for tourneys and spire already, we have individual contributions listed for both of those events, why would a FA be different and not deserve the same kind of recognition?