I would love to see some Power Armor Exclusive Unarmed Combat Moves/Kills. Imagine picking up a Raider by their head with one hand and then crushing it, punching their head clean off, knocking them down and then stomping on their head, ripping off a limb, throwing them out of your way or just straight up crushing them by landing on them in Power Armor.
There should be a climbing ability in the Fallout Games. What if you could scale tall buildings to find hidden treasures or climb over that pesky rock that stands between you and your objective?
The ability to become a Ghoul or Super Mutant. These would obviously be leveled out, like Ghouls are immune to Radiation, Ferals won't attack but can't enter certain Settlements, but there could be Ghoul-Only Settlements where Humans aren't allowed, but Ghouls are. and can be damaged easier. Super Mutants have superior Strength and Damage resistance, but their Intelligence and Agility take a hit. Also, like Ghouls, they can't enter Settlements, but can enter Super Mutant Settlements. There should be someone in the Wasteland who could cure them, for a fee.
A dynamic weather and seasons system, with Overheading and Overfreezing. This will add a new way to experince the Wasteland. You would need to dress for hot and cold weather, as well as climate control your Base of Operations. A Campfire and a warm jacket can keep the cold at bay, while some fans and lighter clothes would prevent heatstroke. Being too hot or cold would drain your AP and eventually Health.
I don't know about you, but I would like the ability to repair Vaults and make them your own Personal Base or let other people live with you. I know Vault Tec Workshop exists, but I'm talking about fixing already established Vaults, not building one from scratch.
Buyable, Craftable, Stealable or Repairable Vehicles would give the Player a new way to travel the Wasteland, probably could eliminate Fast Travel with this.
(Edit) Someone commented that Fallout should adopt the Skyrim style of skill system and I could not agree more. I always thought the old skill system was kinda stupid in my opinion.