I think if want to replace the attribute points on level ups, they could do like these
Melee Damage - govern all damage from melee weapons
Range Damage - govern all damages from ranged weapon
Magic Damage - govern all damages from magic
Health - add health points
Magicka - add magicka points
Stamina - add stamina points
Then give two or three stats above to choose on level ups
While the skill progressions maintain from Oblivion with some upgrades/improvement, example
One Handed
level 15 - deal 10% more damage
level 20 - can use standing power attack
level 25 - deal 15% more damage
level 30 - can do forward power attack
level 35 - deal 20% more damage
level 40 - can do left and right power attack
level 45 - deal 25% more damage
level 50 - can do backward power attack
level 55 - have 20% critical chance
level 60 - have 20% critical damage
level 65 - have 20% chance of decapitation
level 70 - standing power attack have 20% chance to deal bleeding damage
level 75 - left and right power attack have 20% chance to disarm
level 80 - forward power attack have 20% chance ignore target armor
level 85 - backward power attack have 20% to paralyze
level 90 - deal 30% more damage
level 95 - have 30% chance critical hit
level 100 - 30% critical damage
Destruction
level 15 - able to cast novice magic
level 20 - novice magic deal 20% more damage
level 25 - novice magic deal 30% more damage
level 30 - novice magic cost 50% less to cast
level 35 - can cast apprentice magic
level 40 - apprentice magic deal 20% more damage
level 45 - apprentice magic deal 30% more damage
level 50 - apprentice magic cost 50% less to cast
level 55 - can cast adept magic
level 60 - adept magic deal 20% more damage
level 65 - adept magic deal 30% more damage
level 70 - adept magic cost 50% less to cast
level 75 - can cast master magic
level 80 - master magic deal 20% more damage
level 85 - master magic deal 30% more damage
level 90 - master magic cost 50% less to cast
level 95 - all destruction magic deal another 20% more damage
level 100 - all destruction magic cost 70% less to cast
* about stagger and such, it can be governed by other school OR type of magic it self
And so similar with other skills. We gain all these improvements automatically when we trained for it, In this way we really "getting better in what we are doing and what we have been trained for"