This may sounds kind of stupid, but what exactly is the function of levelling? I mean, let's say your character hits level 50 and so cannot activate perks any more, what does being level 92 at lock picking for example do? If you can't get any more perks then does levelling up your lock picking still make it easier for you to pick locks somehow even without perks? Or what if you want to create dragon armour but have used all of your perks on other things? Does getting your smithing level at 100 still allow you to do that?
This is without mods, mind.
Each "level" is the point at which you are awarded one more Perk point and your choice of +10 in stamina, health, or magicka. Leveling also has an impact on what you'll find in new caves and dungeons since there's a small amount of encounter scaling in the game.
Skill levels still matter even if you're not perking. A 100 lockpick skill is way better than a 75 on any given lock in the game, even if you have no perks. In the case of smithing, the ability to create armor is a function of perks, but the amount any given armor (looted or created) can be improved is a function of your smithing skill.
Hope that helps.