I have a theory on why Jaune is the only character in the entire series (that we’ve seen fight) that fights wearing armor. Or more accurately, why everyone else (except maybe Pyrrha) goes into battle dressed in cloth that offers little to no protection.
We’ve been told that Aura is a manifestation of one’s soul, and that you “project your soul and your self when fighting”. We’ve also been told that the creatures of Grimm are soulless and the “manifestation of anonymity”. Pyrrha also claims “they are the darkness, and [humans] are the light” but everyone has a little of both. It stands to reason that anonymity is also closely tied with darkness, and that individuality (or whatever you would call anonymity’s opposite) is tied to the light.
If light is tied to individuality and anonymity to darkness, then it’s plausible that anything that reinforced that you were an individual would strengthen your soul’s light side and anything that reinforced anonymity would strengthen the dark. And when you strengthen your soul, your Aura strengthens. Since all of the characters’ weapons and equipment are conduits for Aura, this means that their weaponry becomes stronger and more useful. And as we witnessed personally, Aura can also shield you from harm and heal your wounds. So the stronger your aura, the stronger you are.
To make a long story short (too late): Aura users dress in impractical-looking ways because it’s actually very practical – it makes their “magic force field”, their weaponry AND their ability to heal stronger by reinforcing who they are. Such an enhancement to their abilities, both offense and defense, does more to protect them than armor ever could. Jaune wears armor because he doesn’t know how to use his aura.