I understand that the biggest worry in a sprint is scope-creep so you wouldn't normally want to do this. However, I've occasionally started a sprint and then realized that there were a few stories we forgot to estimate story points for. Now I can't add that without completely screwing up the burn-down chart.
I understand you're trying to encourage best practice here, but now I can't actually follow those practices because of the restrictions in place.
Am I missing something?