I didn't read the OP, or the replies but the subject was self explanatory.. Sorry if it has been pointed out, as I am in a rush.

The armory system in a far-fetched way already opens this up to being a possibility.

If you look under the description of a weapon, it doesn't specifically say it's a "sword" (aside from the title of the item), it says "Gladiator's Arm", as an example..

This is already shown with CNJ & THM, where both classes can equip clubs and staves, yet the class that supports them is described in the finer print.

In future (let's presume the multi-job system is going to happen), I am sure it wouldn't be difficult to have say a "Scythe" for LNC and call it "Dark Knight's Arm" (as an example).

The only issues I can see with this are the animations for certain skills are fairly distinct for the weapon they are using, although this could potentially be modified in the future.