It's broken in the fact that it's basically "buy more games, get higher score" That's just not right, why should you assign what cool things you've done in different games to one score? It would just work a lot better if it assigned the scores to the games they apply in. It's also broken because some achievements may be labeled as hard when it's actually really easy, or vice versa. You don't get scored in space invaders by how well you do in donkey kong. You're not getting the per game concept, I'm saying that you get scored for each game, then that is displayed when you compare achievements. (And why does microsoft limit every single thing on the xbox? I've never really gotten that? can't developers make their own game?)
That's not being broken. Broken implies a lack of functionality, but gamerscore works perfectly fine for what it is supposed to do. You're missing the entire point, it's not supposed to be that in-depth, it's not a fantastic scoring system, it just talleys points gained from achievements. That's it. That's all there is to it, it just counts achievements.
Also to respond to the boldened bit:
That's irrelevant for two reasons:
1. Regardless of the achievement, you can only get 1000 points from each game.
2. I'm pretty sure they moderate the achievements a little bit.
and to the ital bit:
I don't understand what you mean by this. It's simply not coherent.