Here's one idea. Drop the leveling and keep the perks. Start with a blank slate, but have nifty titles that come with accumulated perks, such as 'Great Warrior', 'Notorious Assassin' or 'Renowned Wizard'. At lower 'levels' you may collect a few titles (lesser mage, wanted cutpurse, accomplished swordsman) as you dabble in different trades. But as you specialize and develop, you can reach greatness in a particular 'class'. There's no need to put a number on these levels for the player's bragging rights and it would be more immersive.
Again, they'd have to do away with scaling so that your 'Master Swordsman' doesn't get whacked by some sewer rat, but I think it would be closer to actual role-playing while still satisfying min-maxers. You'd still have pressure to improve yourself and 'beat' the game if those are your goals, but it would take out the focus on math and make character development more fluid.