There's too many skills with too high cap. It encourages alt usage and makes too one-sided characters. It also makes the wasteland pretty irrational place when people run around with super high tech miniguns and energy weapons just because big guns and energ. weapon users need to have their guns. In addition the current skills are from very old singleplayer game, where level cap was 99. Even Chris Avellone stated that the fallout 1 and 2 skills weren't that balanced but were better in fallout 3.
Source.
Therefore we could take an example from Van Buren and fallout 3 skills.
It could be something like this:
FA&doctor -> medicine
energy, big and small guns -> firearms
Melee weapons&unarmed -> Melee
sneak&steal&lockpicks -> Thievery
Throwing&traps -> explosives
Barter&speech -> Diplomacy
Outdoorsman
Repair
Science
Gambling
In addition reducing the cap of skills to perhaps 200 would be sufficient. Players would not become jacks of all trades because you still can have only certain ammount of profesions and perks.
The bonuses would be various:
+ Less reasons to create alts
+ Players could take part on much more activities without being completely self sufficient
+ High tech guns could be made rarer and their roles could be changed
The downsides would be
- It would require lots of re-thinking and balancing