So I got to thinking: how could this problem be easily alleviated without modding or a making significant change to the leveling system?
Well, what if, after acquiring all the shouts in the game, you were able to to exchange X amount of dragon souls for a perk?
For example, say I have every shout. I can then purchase any perk of my desire (though still following the branching system for skill perks) at the cost of say...5 dragon souls.
What do you all think? Sound good and whatnot?
To those who argue specialization over universal proficiency in skills, I say this:
If Bethesda really wanted to make a specialized character, I shouldn't be able to become the leader of every guild and faction, the hero for every Daedric Prince present, and Dragonborn! ...surely this makes sense.
In this context, and in the context of all previous Elder Scrolls games as well, a truly "specialized character" is impossible. The very nature of this series advocates being a jack-of-all-trades, whether or not one can acquire every single perk. While this mindset admittedly can work for Fallout, it fails in Skyrim. The limitation of perks only hinders the player from what the game itself wants you to be: a master thief, warrior, and wizard - all in one.

