Yes simply have 1 'armour-skill' and then your character will have penalties after your playing style, meaning weight mostly..
It seems to me that having only one armored skill defeats the purpose of having armor skills at all, unless you use perks to allow the player to specialize in certain types of armor, because the main function armor skills served in past games is that you could choose the armor skill you want, and would benefit most from going with it, so if you wanted a lightly armored character, you could choose light armor and stick with it, if you'd rather have heavy armor, you could go with that instead, I mean, armor skills improved your defense with specific armor types, but that was just so there would be a point in using the armor type you specialized in, if your going to remove the distinction between armor skills, there's really no reason why you can't just scrap armor skills entirely and have armors just provide a static amount of defense, other games seem to work just fine with this, either have at least two armor skills, or do away with them entirely I'd say.
Even if armor skills are removed, though, I'd still say there should be distinctions between light and heavy armor, leather armor still needs to have diffferent advantages and disadvantages from steel, just because there's no skills for armor doesn't mean you can't still put them into different weight categories, New Vegas for example had light, medium and heavy armor despite lacking armor skills, with heavier armors causing penalties to movement and sneak, Skyrim could do something like that too, if armor skills are gone.
Regardless, though, Skyrim can have more than one style for the same material too, this doesn't have to be just for different armor categories either, rather than just steel, you could have Nordic steel and Imperial steel and so on, and these could either be items that have the same stats, with the differences being purely cosmetic, or they could have different stats, after all, material isn't the only thing that would effect how much protection armor offers or how heavy it is.