So, one thing that I've run into after watching 21-ish hours of commentary on Morrowind and Oblivion is that there's a key and major writing handicap of the last two TES games: The main quests have far too much urgency from the start and confirm the importance up-front, whereas Morrowind's story doesn't really have urgency since the problem's been going on for decades and you have to very firmly prove yourself the Chosen One in question before the game treats you as such.
For Oblivion, my most immediate thought is having the tutorial "dungeon" separate you from Uriel mid-exposition, such that you catch what the Amulet of Kings does and that a hidden bastard heir exists, but you don't have directions to Martin nor the amulet itself.
Then the main story picks back up with Kavatch, with you looting the Amulet off a Mythic Dawn middle-manager you prevent from killing the last officials of Kavatch and the Dragonfire going out a few quests after that only giving immediacy a large portion through the plot.
If you fish around and save the right important persons, you get the information that the Amulet was abused to make the first free-standing and abrupt Gate, with the available spawn locations prior to the Dragonfire fully extinguishing all being attached to Daedric cults helping from the "inside", as it were.
Skyrim needs a total overhaul of the mechanics for learning Shouts for this to work, though. Throw in Dovahzul books taking up the role of spellbooks to unlock them, with additional per-Shout proficiency from doing or experiencing what the Shout does (e.g. taking or dealing fire damage for Fire Breath), then Dragon Souls act as the "trainer" for this.
After that, give Alduin a schedule for the burial mounds, stealing notes from the original Fallout about having some Bad Things happen if you go long enough without killing Dragons. Mirmulnir takes up Alduin's place in the intro, giving a Dovahzul speech that, when translated, makes it clear he thinks Ulfric is the Dragonborn.
Then the tutorial previews to you what a Thu'um-backed Warrior looks like with proving this is not a farce by having Ulfric scripted to rip through Legionaries on your way out, either path. In this rewrite, you fail the main quest shortly after Alduin hits Windhelm. But if you know how to pick it up later, you turn it into a race against Alduin and Ulfric.
...Overall, I'd love Skyrim to touch on lore about how prophecy works. It happens, but who does it is up in the air. Somebody is going to be "The Last Dragonborn", but if you feel the desperate need to sequence-break just to see what happens you can go ahead and put Miraak of all people in that position, getting a hilariously over-the-top speech for the trouble.
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And since I'm rambling extra on Skyrim, I'd love for Thu'um to cost Stamina and Magicka instead of being on a timer, so neither Warriors nor Mages can ignore the other's resource, while Thieves have a very touchy cost-benefit analysis about when to use a Shout when being a Stealth Archer.
Another thing I'd like would be redoing Enchantment with a return of Morrowind's numeric soul value and on-use effects, but not item capacity. Instead, the limit is based on the gem used and your skill level, with enchantments staying separate from spells, and the big "selling point" is modifying existing enchantments with some loss offset by the soul used.
The two "points" are streamlining the cast-by-proxy setups with staves just being a valid target for both weapon and on-use enchants, alongside making it so that experimentation with enchantment is easy and cheap as you don't need to get a new item nor a replacement Grand/Black soul.
Ideally, this turns into the ultimate super-enchants being something you build up with a large pile of Grand souls over time, making you interested in getting a good base item early to shovel souls into with diminishing returns. The point is that the uppermost edge is a predictable diminishing return so that a JRPG style degenerate superboss can actually work as intended.
Also add durability that cripples, but does not break, the item in question, with Smithing getting a good chunk of value from added durability just like Oblivion Armorer. Same "diminishing returns from dumping further resources into the item" scheme as above, few sliders to tweak the balancing of what you're forging, bake into the creation process.
For alchemy, more effect value variance in ingredients, and a return of the alchemy set components but as variables to adjust. Rather than removing negative effects, any effects separated end up the other kind of item. Further added would be re-mixing potions and poisons to shuffle effects with some losses, alongside Favoriting formulae to automate the process.
Sounds like a hellish to implement setup. My suggestion would be a three-column matrix of the effects, their magnitudes, and their costs on the item, with each effect referring to what value to apply the cost to. A set number of each kind of "slot" on the item would be easiest to implement as it makes the diminishing returns into predictable matrix multiplication.
...Rant over...