Narrative , Pacing and Leveling Up

There are things about D&D that bug me. Certain artificialities that break the spell of fantasy and remind me that I'm playing a game. One of those is leveling up. I'm sure that it was the first thing to be copyed in the online versions of roleplaying. It always seemed so odd that as soon as you hit a magic number of experience points then "bing" you are instantly better at everything and can sustain more damage in combat. There have been a few Dragon magazine articles and such about how to make leveling up more realistic but that's not really what I'm looking for. Not realism, but a sense of fitting in to the story of the characters. I like to look at the adventures the party has as a story. And the instant nature of leveling up doesn't match with that ideal. Most of the options for leveling up call for some type of training to be paid for and undertaken. Usually in a town where the party finds itself. That gave me an idea. What if it wasn't training per se but a side quest or ordeal instead. And it takes time, and at a place far away from the party. The party splits up for a time and goes their separate ways. Later, (weeks or months or perhaps even years) have gone by and the party gets back together. They have spent all the loot , (maybe on a drunken orgy or two) and are now broke and need to go adventuring again. They meet up and swap stories about their time away. Players should feel free to create whatever backstory they like to fill in this gap. By creating a time gap in the narrative it creats a more epic story. Instead of going on one adventure after another like an assembly line they have periodic adventures. It always bothered me how PC seem to reach high levels in only a few months whereas NPC take years to build up that kind of experience.
Maybe something like this has been suggested before. But for me the crucial elements are time away from the party, a measure of time passing and the backstory the player creates. A crafty DM can even award extra magic items and spells or other things based on the PC's tale. Maybe there can be more to a charcter's life than bashing monsters and taking their stuff.