TESO is a trinity MMO and it has roles.
Saying that, you can use any weapon and wear any armor that you want but their are penalty doing so. A warrior using a staff will only have access to two of the skills of that weapon and they will not have access to the special skills that staff would give a mage or a caster. You are never going be as powerful as a mage would with that weapon, the same goes for a mage wearing heavy armor.
If a mage wears heavy armor then he will not have access to magical stats that wearing light armor would give. Fact is you are at your most deadliest wearing your class armor and welding your class specific weapon.
If i play a rogue and decide to use a bow then i will have a light bow skill and perhaps a heavy bow skill, i would only use the bow to pull or kill runaway mobs or if i'm above another player in PVP. I draw the mob in with the bow then i go to work with the weapons that will make me as powerful as can be, they are daggers.
While I agree with this, I do recall hearing that, even if you don't get the bonuses, and all that stuff, that does not mean you will be useless doing those things, there may be situations where going in to melee is pure dumb, so a warrior can shift to a bow.
They clearly stated, that it WILL do damage, of course, as Sheek said, it won't be optimal, but it WILL be noticeable damage/heal.
My point would be that its not just for the look that you are able to do that, from what I understood, you are effective doing other things outside your class range, so I just wanted to let people know that its not just for the visual, it can actually be a tactic to employ, and not be useless at it.