Nope! As weird as I thought it would be to equip Balthier with anything but a gun, I had him using poles quite early in the game.
Vaan was, over the course of the game, equipped with every type of sword under the moon (by XII's standards), though I think I've got him with the Save The Queen right now.
Fran, I kept her using bows. I wanted to keep a long-range character in there. She was also my main healer.

The above was my main party, but I also ended up making Penelo use staves... even though I never used her. Just for kicks I guess. She was originally going to be my summoner, before I realized I would never use her.