"What would you do to improve the combat of the TES games?"
Oh god, everything. The TES games have always had awful combat and progression systems, mainly because they were completely broken/unbalanced but not in the way you want single player games to be unbalanced. In Oblivion, the optimal strategy was to tag skills that you *didn't* use in order to artificially depress your level. Fortunately they ripped that out for Skyrim. But Skryim's problem is that you were in a "worst of both worlds" situation in terms of generalist/specialist. Basically you were defined by your weapon choice, but there was nothing particularly stand-out interesting about say picking a sword over a mace. Just minor differences that didn't matter a whole lot within the context of the game world. The big split was melee/magic/ranged (which is the same meaningful split in any stock fantasy game). Basically it works like this...
Classes = strong identity, but limited connectivity
Classless = weak identity, but combinations can get super interesting
TES gets the weak identity from being classless, but making up your own combinations isn't interesting. This is the worst of both worlds. Typically in a single player game, this is where you find the "lol I combined X Y and Z and used my fire magic to put an explosive countdown on a guy, and then knocked him back 50 feet with my mace into his friends and blew them all up!" Single player games are fun exactly because of this kind of imbalance. In MMOs, or games with a multi-player component, you are a lot more limited to the "3% more damage... yay..." type stuff because the gross imbalance in single player games that make it fun also make it very un-fun for everyone around you in multi-play. So it's almost like they balanced it to be an MMO, but they really messed up on some of the additive bonuses so it still comes out broken.
Basically to improve combat in TES just pick a direction and mitigate the negatives, as opposed to getting into a worst-of-both-worlds situation. Personally, I would find strong themes/identities between all the weapons, figure out how each weapon has synergy with everything else in basic terms, design strong abilities/attacks/spells that stick to the theme, and let players figure out the interesting combinations that may be completely broken in silly/exciting ways. And then just make sure there is enough monster-variety that the player can't be a 1-trick-pony all the time (what's easy for player A might be hard for player B).