I think within reason that this is a viable idea.

But for the most part, no, leave it as is.
I enjoy that when I switch to my GLD, my character doesn't magically forget everything he knows about spells just because he has a sword in his hand instead of a scepter. Just like (and I know this will change soon) I don't think it makes much sense to have a ban on what gear you can equip at certain ranks.

The old argument: "Oh, I'm level X. I won't understand how to put on that boot on my foot until I'm level X+2." comes to mind.

Skills are the same way.

"I've trained for ages as a CON. I'm a master of the elements. Awh, damn. I can't use my knowledge because I have a lance in my hands."

And to an extent, this should be true, I agree. But it's already implemented. A THM can't Multi-Shot, because, well...They don't have a bow in their hands, and somehow multi-shotting out of a staff seems silly. If they locked the WS, then they limit the classes which are supposed to be very mix-matchy and open. Jobs, hell yes, limit the mess out of them. But amp up their power with their stricter ruleset.