It's not completely straightforward. The deceased person might have sent or received emails that they really wouldn't have wanted their relatives to see. Or someone might have sent them a confidential email containing information that they assumed would not be seen by the relatives.
That might be for something trivial, but it might also be something really critical.
Maybe the emails could be checked by a third party such as their lawyer, who would only pass on essential information? I've no idea of the legalities involved.