Yes, there is that obvious route. But Blizzard depends a lot on other players reporting the bad behavior and taking a long time to investigate, and who is to say Blizzard Entertainment has been provided truthful account information by the account holder? It just seems to me that they (the violators) could claim it was not them at the time. Does the law compel them to provide the wrong-doers?
It's a bit of a nice idea, but has some practical issues.