I haven't had a look at the d20 CoC yet, so I can't compare, but I've played the original system and I like the sanity point idea (did they keep that for the d20 system?).
Something like that would allow for the GB idea of “Ray's gone bye bye, Egon. What have you got?” Ghostbusting isn't about dying anyhow, but they do get frazzled sometimes. Peter's “he slimed me” moment is a perfect example of a character blowing their sanity roll and becoming useless for a bit. The same goes for Winston getting run over by the ghost train, or Egon retreating into his calculations when they meet their first ghost.
There are a number of games that do something similar to what you're describing with making action points rechargable. The few that come to mind use a system where certain skills are linked to your action points and when you successfully use them, you get a point. There is a cap on these points, so you can't stockpile tonnes of them and overwhelm the rules. I'd imagine for a d20 system you might want to limit it to naked rolls, rather than rolls where people apply bonuses, take 20, or are aided by another character. On the plus side, you now have the possibility of a new feat, where the action point limit is increased by a point or so.
Just some thoughts.