I mention what Todd Howard said because it partially touches on what I am proposing. I think that we should see the visual representation of our skills for now on. Even Skyrim has a stat sheet approach to a certain extent. When you swing a sword at level 1 it looks the same as swinging a sword at level 80.
So imagine this. If we are level 1 and have a fairly low one handed sword skill then our sword swinging animations will look very much look like an amateur when it comes to technique. So the enemy can easily anticipate your moves and either avoid you or block you(Imagine if the enemy laughs at you and taunt you because how weak you are). But as you start to progress your swinging gets more precise, you start to swing faster, you start to do more advanced and complex sword moves Until reaching the point of master swordsman.
This can work with other skills too. But first Bethesda would have to add a hell of a lot more animations. For example we should see our character whip out the mortar and pestle if in the field when trying to mix a potion together. So if we are bad at alchemy we could see that the potions start to react badly. Like the liquid may overflow the pot, or maybe erupt from the pot like a volcano, or if you do a really bad potion it could blow up the pot right in your face.
I can go on and on about the different skills with examples of visual representation, but I think by now you got the point. So the point is to actually see how bad we are in the beginning so we can see our characters grow. I think it would add so much more to the experience and so much more satisfaction as we get better.