Someone, sometime, somewhere down the line decided that certain abilities should be tied to levels. These abilities are not necessarily related to combat skills (which advance as a character advances, because the character practices them). They are things like Proficiencies and Inborn Character Skills that expand, are expounded upon, or become more useful as a character increases in level.
The simplest question to ask is this: does experience in combat equate to experience in all other aspects of life? The clear is answer is no. Why should only 15th level priests be made hierophants of their faith? Why should certain spells be available to 15th level adventuring priests and not their 1st level (or 0th level) administrative counterparts? For example, a priest who has never adventured a day in his life but is a politicker of great skill might run an entire faith—does it make any sense, really, that simply because he's never gone out and swung a mace that his deity would refuse to allow him access to specific and powerful magics?
While a case can be made for the administrator/leader role (and a counter case might say that no, in fact, that deity would probably grant his chief follower the spell just as if he were a level 15 priest), there is no such case for NWP advancement. Skills, essentially, are not functions of combat experience but rather experience at using that skill.
Should there, then, be a system in place that allows characters to advance skills without gaining levels? Most probably. What would such a system look like? Here's just one example:
Every six month period spent studying a skill provokes a check: roll a d20 (with some appropriate modifiers based on circumstance - additions for teachers, subtractions for lack of materials or inconstant study). If the check succeeds you learn nothing knew. If it fails, your rank increases by one point.
Simple, perhaps too simple. And yet, doesn't it make a nice compliment? Now, while your party wizard is out studying the secrets of the stars and concocting spells, you can be learning how to play the lute.