Ok, 1st of all, The item on the back of the coat is called A Baldric.

A Baldric is a Belt used to hold sword Scabards, Bare Swords, Hand Axes, and in some cases tools.

Since it IS a belt, Cloud can (And Has) taken the belt off when it was inconvenient or unessicary and FF14 makes the Sword Belt fall into the later as it serves no function.

It clips Most Weapons, Almost All Shields, and several Character Moddles such as Au Ra and Miqo'te.

I'd prefure it removed because Clilling is annoying and I go through Great Lengths to choose Glamours that dont clip. Which is sad because this is my Favorite Glamour yet and the Belt exists despite cliping and it's uslessness thus taking away from the look.

And I think resorce wise the belt not being there would likly remove some stress by making it simpler to render.