We used to have a glory score, along with infamy and two other stats I think. I don't remember why it got ditched, but I think part of the problem was precisely to make it a meaningful stat that reflects reality, which I think it did poorly. Any introduction of such a score also needs to be given time, because it's hard to give a proper stat value based on events that happened before the stat existed.
If it is too war-centered, it also becomes pretty close to stats we do already have, which are H/P. These only reflect the past, though, and not the present. A lot of the really inactive guys do have high h/p. Often, they are the ones with the most of it in the realm... Which is why, while I like Indirik's ideas, it must be considered that oldies who just follow orders into battle don't necessarily make things fun, though at least they are taking risks and participating, which is already better than many others.
Perhaps in place of (or in addition of) such game-generated stat, we should have a player-driven one? In this regard, we already have medals, but these only reflect the past, target the player as a whole, and don't actually have any effect. Perhaps characters should have an option to rate other characters in the realm? A few metrics could be used, such as trustworthiness, respectability, leadership and fun. Bonuses and/or new actions could be granted, according to some of the scores. For example, someone with a high fun score could passively see a percentage of the fines he gets payed by NPCs. Someone with high fun and leadership could use that usurpation feature suggested by Lorgan against someone with low scores in the same stats. Characters with high respectability could band together to force destitutions of government members. The like. I'm not 100% confident we can trust players with this power, though.
Edit: for such a mechanic to work, there would need to be some bonuses or actions that are no longer possible when a certain stat goes too high, otherwise cliques are certain to give each other max scores in all measurable stats.