Your chocobo does contribue quite a bit on damage. it was really noticable for me as i lvled up my paladin. without it would take me 2 halone combos to even break the mobs hp to half, with my chocobo it just takes 1 combo to get it down to 2/3 so yes its very noticable.

As for the idea i support it. More things to do even if solo or with another friend with their chocobo would really beat just grinding the crap out of mobs since its all that we can do to lvl it.