I will be adding things to this list, hopefully I'll bring something new to the table.
1. You should get a starting weapon based on your stats.
Instead of always starting with a pistol, you get a starting weapon for the highest offensive skill.
Should also apply to grenades, mines and such, as long as you have enough points invested in them.
2. Repair kits (should be affected by mechanics/electronics skill and indirectly by mercantile).
Instead of repairing a fixed amount of durability, it should repair based on the value of the item.
For example, let's say a weapon has 300 max durability, and when fully repaired is valued at 10000 credits. If the gun is at 30 durability, and is valued at 200 credits, the basic repair kit will repair 1000 credits worth of durability when used on it, bringing it to 70 durability and value to 1200 credits (numbers are made up).
What will this do?
It makes cheap starter weapons cheap to repair, high-end stronger expensive weapons very expensive to repair, mechanics/electronics to affect repair kits (e.g. 1 point in the skill increases the value which a repair kit repairs by 1%) and mercantile will reduce the cost of the repair kits indirectly increasing the repair/cost ratio.
Last but not least, it'll make "found a gun in low durability, sells for 200 -> buy a repair kit for 900 -> repair gun making it worth 3000 credits" available only to those with high mech/elec/merc skill.
3. More secret areas.
I've been running around with 10 perception (7 + 3 from trait) and I've only come across 1 hidden door after the initial trap doors in the outposts quest area.
4. V.A.T.S. style targeting.
I will refrain from using sexual innuendos in describing how awesome it would be.
Practical reasons:
Means that Psi is no longer just another gun and psi boosters the ammo, if you can aim where you shoot and not where you Psi.
5. Allow the player to beat Ezra in a contest of the mind.
Not necessarily becoming more powerful than him, but with enough will and thought control, one should be able to capitalize on the moment of surprise Ezra had, and beat him.
6. Different beginning.
You should never separate the player from his avatar, the discussion in the room at the start makes no sense, I shouldn't know what they're talking.
New start:
they haul your ass to their base from some place you've never left, which would explain why you're absolutely oblivious of the world outside.
Earthquake hits, damages your original home's defenses and riles up some mutants who migrate and destroy everything in their path. Everybody's dying and you escape with whoever's left, blow up some tunnels behind you, trapping the mutants there, at least for now. Thanks to being ambushed by rathounds and other beasts you're left as the sole survivor (point is you have to be the sole survivor because you can't have any past connections anymore). You get found by Gorsky's team and they bring you to SGS, and eventually you go through Tanner's tests and are accepted as a member.
Could also be that a diplomatic team from SGS was already at your old home when the earthquake hit, explaining how you escaped to SGS and not having the need to explain anything.
Or you emerge from your growth tank and go from there.
7. Unique weapons.
go through the toughest monsters just to get that Billy-Bob's 5mm pew pew or Bruno's electric crowbar.