+Courtney Campbell and +Jack Mack wrote some interesting posts about D&D, the area that piqued my interest (for the moment at least) was inspiration. Read the articles, get an understanding about what they're trying to say. Mack isn't keen on the extrinsic wear and tear on the players, Campbell its subjectivity. Heres why I think you shouldn't worry about those things and present another angle on the mechanic.
This edition is the game of many faces, lots of different things from lots of different games. Some d&d and some not. WoTC has taken great pains to make anything they include feel appropriate and 'classic' but really its clear they've been looking at their peers and the multitude of popular 'indie' games that have blossomed since the OGL and 4e.
Inspiration = Fate Points
Personal Characteristics = Fate Aspects
If your familiar with Fate, hopefully you've had either an "Aha!" or "Yeah... obviously!" moment, if not let me give you a rundown. Aspects in Fate act like the gears that drive your character, you can turn them to add drama to the game (usually, but not always, creating complications) thusly earning tokens which can be spend toward enhancing rolls. They're like disad's that you can summon when its most interesting to. Like every good disadvantage, it gives you a boost elsewhere.
When you look at D&D's inspiration like this the extrinsic reward becomes less problematic, still if your not sure try this. So my players are roleplaying anyway - lets harness that energy in a different way to drive another part of the system -Why cant I turn those gears? I want to call upon character traits and offer inspiration in reward for a complication or interruption of my choosing. This way I can make things more interesting just when it matters. Still let the players have control, but when you want your able to lean across and grab the wheel, just for a moment.
Suddenly inspiration is acting more like XP, and hopefully less extrinsic.
Subjectivity is hard. I don't think I have a concrete answer here but I think i'm close. Its about relationships. Indie mechanics often rely on group support to work, theres a lot of power shifted toward players and away from the referee, this shared responsibility is really rewarding for the players and takes a lot of the burden from the ref's shoulders. But runs kind of against the grain for the old school dungeon play that this edition runs with.
You (or you're DM) will figure out how inspiration makes an appearance at the table. But first? Check out Fate. Hopefully you'll look at it in a different light.