First off, being Dragonborn is the most central aspect of this game and much is made of your ability to absorb Dragon Souls. We all know you can unlock shouts using souls, which is the only way to utilize this extremely valuable resource. In many ways, the Dragonborn is gaining power by absorbing Dragon Souls, but this is only really exhibited by the unlocking of more shouts, which you can only use 1 of at any given time. What if we could use dragon souls as more than just a resource for unlocking shouts? Here is my idea.
I would like to see dragon souls used to unlock perks. You will still level up as you raise your skills and select an increase to health, magicka, or stamina, but you will no longer select a perk. Perks will be unlocked solely by spending dragon souls on them. Perks will still be skill locked, so you have to have the appropriate level of skill to unlock the perk, but you will no longer have to spend perk points to move up through the tree. Take Heavy armor for example, instead of spending 2 points to get to the Conditioning perk, you can instead wait until you hit skill level 70 and then spend a dragon soul to unlock it. In conjunction with this new system, I think it would be a good idea to either 1) limit the overall number of perks you can spend (such as at 80, which is the current max, or maybe bump it up to 85 or 90) or 2) make higher tier perks cost more souls (based off a function of the skill necessary to unlock the perk, such as: [soul cost = (skill level/10)-5] or whatever works for balance). Once the player's perks are capped, maybe dragon souls could then be spent to raise a players health, magicka, or stamina by 5 points per soul spent, or maybe even 1. This would give soul collecting a useful purpose past capping perks and unlocking all shouts.
The idea is to keep the level of perk progression from being too fast, if that would even be a problem with this system, which will both remove the annoying need to grind skills outside of your primary play style as well as give you a challenging decision to make when choosing how to spend your souls. This will also give players incentive to hunt dragons down more actively than they maybe did, and give dragons an even more prominent role in Skyrim, not to mention it will help give players with a huge collection of souls something to spend them on.