I'm of the belief that the problem is tied to D&D fluff/culture first and foremost, so that needs to be adressed first. If you change people's mentality from Warrior = Guy Who Hits Good With Sword to Warrior = Guy Who can channel Chi / Grit / Spiral Power / Being So Angry He Can't Die, then making them able to fly, punch through magic or stand so incredibly still that they become invisible to the eye (hello Drax!) starts being acceptable. Then you can cook any spell-equivalent ability your heart desires.