Even though we do not get accolades for the characters we have in Trap Team, it is still worth scanning them all in for several reasons:
1. Your elemental power does go up for each different character of that element you add in.
2. There are only 99 hats in this game - the rest are carry overs from the previous games. So if you gotta have them all, you are going to want to put hats on your characters in the earlier games, then summon them into Trap Team, making the hats now available for all your new characters by unlocking them in this game. This would be worth it for some of the best hats, like the ones from the adventure packs.
3. If you have the 3ds version, you only have to scan each character in once to have them available for play anytime without using the portal again (though you will want to put a character back on the portal to update it if you played it a lot in the 3ds version, or to make your 3ds character the same level as your character on the console version).