I don't think it's helpful, the language of mystery and mystique, that keeping something shrouded in secrecy is a good in itself...I don't mean to say that. We lawyers tend to be a rather cautious lot, so I'm reluctant to recommend a very large change like that.
However, more importantly, in circumstances where the Governor General refuses the advice of the Prime Minister, the focus is then removed from the Governor General. What seems to me to be important, then, is what subsequently happens in the House; when the advice to the Governor General is refused, things are sent back to the House of Commons, where the House can take what steps it will.