I agree that it could be useful to allow extra settings to give finer-grain control over when the student can see certain answers / scores /feedback etc.
As well as your suggestion to allow students access to information only after they have used all available attempts, I would suggest another category 'while attempt open'. This is a less common scenario that arises perhaps when the student browses away from the quiz page during an attempt, and views mod/quiz/index.php or mod/quiz/(re)view.php. Currently this scenario is lumped in with 'immediately after quiz' (v1.6) or slightly worse 'later while the quiz is still open' (<v1.6).
Overall, a good idea, but it would be interesting to decide how conflicting settings are resolved: eg if all-attempts-used and immediately-after-attempt settings both seem to apply -but conflict- which is used?
Perhaps you want to file a feature request, and then maybe develop this feature yourself