I'd like the non-magical classes to start with mundane skills, but scale them up to the mythic level. Like:
1-6: Mundane, within realistic human range.
7-12: Superhuman, but without violating basic physics and psychology
13-20: Styled as "not spellcasting", but might as well be magic
So, at level 9 I want to jump onto a three-story building, shoot someone from twenty paces while blindfolded, sneak through a well-lit room with several guards in it, read details of someone's emotions from their body language or bluff them into revealing an important secret, open any kind of lock in a minute, improvise some explosives in av evening from what I can find in a forest. Of course, not everything with any character - but a reasonably wide range.
At level 15 I want to visit Moon by climbing clouds or intimidating winds to take me there, shoot someone who is in the next city, sneak into king's chamber while all guards in the palace are looking for me, deduce all important facts of somebody's past after observing them for a minute or persuade them to kill their best friend, walk through closed door, destroy a building by shouting at it.
In game mechanics, it can be done in two ways: either by giving non-casting classes various "powers" representing superhuman abilities (but without limiting most of them to combat, as 4e did), or by reworking the skill system so that skills are not limited to mundane uses. In general, gaining levels should improve and widen what one can do, not just increase numbers.