It's been stated and acknowledged that the current GP system of matchmaking greatly discourages putting any resources into any but the absolute best characters. Not only does it use up the resources but it bloats your GP and pits you against harder opponents.
I have a suggestion. When you join the GA it opens up a screen similar to the TB deployment screen. On this screen you get to choose which of your characters will be included in the GA. Anything you don't choose can't be used and doesn't count towards your GP. Then we're free to advance characters that we like even if they're not very good.
Another possibility is that you set your power threshold. Any character with a power below that threshold won't be used and won't count towards your GP.
I'm just trying to think of ways that don't penalize you for building random characters based on very specific uses or mistakes.