When it comes to TES games, I tend to view classes in one of two ways: Either as part if the character's background, like their training or profession, or as reinforcement of how I want to play. With TES games I think it's far too easy to end up playing a generalist, so giving my character a class label gives me something to play to. So if I decide to play as a battlemage, then before I even begin, I'm basically blocking off parts of the game that I don't think a battlemage should go through.
Personally, I rather like the class system from NWN2. You pick a starting class, but you're not locked into it. You can add other classes, but might be penalised for favouring one over the others, and can eventually choose a prestige class once you meet the requirements, which could be a fusion of sorts of the classes you had. For example the Arcane Trickster, basically a rogue/mage hybrid.
I think that sort of approach could be adapted to work with the TES leveling approach. Your choice of class at level up determines which skills count towards leveling up, and which perks you gain access to, and could even affect attribute growth if they bring back attributes. Even if they just work on a basic fighter, rogue, mage approach, just to move away from generalists, if only a little.
In all honesty I'd prefer the skills not to be connected to level progression, especially where level scaling is involved. But it is the way TES games work, so that's unlikely to change.
Edit: these are just rough ideas, not thinking at my best right now