I like having an unelected head of state with strong power but limited to a very specific range of decisions. The Governor General has no influence over the legislation that governs our daily lives, but does have the ability to step in and make a decision when our elected leaders fail and we're faced with the issue of whether the government of the day still has the mandate to govern.
I prefer an unelected head of state because, if the person were elected, he or she would come to believe that he/she had a mandate from the people and would begin to interfere in day-to-day governance. Our unelected head of state knows full well that he or she has no such mandate.
I'm not so very keen on the Prime Minister being the one to appoint the Governor General. However, I don't know what a better alternative would be.
oh2421, the US does have a head of state. The President. The odditity about the US system is the lack of a position equivalent to that of Prime Minister, and the degree to which the President is involved in day-to-day governance.