Character skill was important in the older RPGs because that was all that could be to make an interesting RPG with the technology at the time.
Not really true. More the opposite, honestly. Character-driven RPGs in general can still work just as well as they before (it's more a matter of presentation and interface than of requiring player skill to play a larger role on that end), but the TES series is in a bit of a unique position where the player has constant and direct control over their character. You aren't giving your character a command to do something, you aren't using a mouse cursor to direct your character on how to move, you are
directly controlling your characters actions and you are
directly controlling their movements. Now, when we were looking at titles like Arena and Daggerfall, this sort of solution looked fine. Presentation involved a lot of 2D graphics and sprites, things like distance and hits were impossible to really solidly gauge and in general the whole "miss something I clearly hit" was more forgivable as a result, so there was no issue there with treating the games like most RPGs. When Morrowind brought them a fully 3D presentation, it more or less killed a lot of the viability of that approached. Having a "ting" or "fwoosh" sound when you swing at a sprite can certainly work as a believable representation of a hit or a miss, but having them when you see your character's arm swing a weapon directly
through an enemy... that just feels horribly awkward. Again, it still works for other sorts of RPGs so long as the presentation is handled well - something like KOTOR can manage misses by showing your character visibly missing with their attacks as you aren't directly aiming or controlling those attacks - but most any approach you could use to try and fix it with these games would end up seeming awkward or poorly implemented.
Character skill was important in older RPGs because a game driven by character skill can be compelling in terms of character building, character differentiation, and more general tactical decisions. It's much easier to make a thief feel different from a fighter in a game where the character's skills are the main deciding factor in success or failure, because that thief will be absolutely useless in a fight and that fighter will be useless in a stealth situation. The TES series is just designed in a way that makes it very, very hard to really maintain that sort of character influence in a lot of ways without the actual gameplay seeming exceptionally strange or awkward. It's not so much an issue with the genre as an issue with this particular series.