More or less a modern day viceroy, yes?
Basically.
It's just that I am so used to our Presidential system where the head of government is a stable, locked in position. Like it or not, at least you -know- who your big boss person is gonna be for the next exact set of years. Seems more stable to me. Whereas in your parliamentary systems, you've just had one political party decide for the whole country that it deserves a new leader on the global stage.
Some Australians do see it that way; hence the reaction to when Rudd was deposed the first time.
However, the idea is when you vote, you vote for a party, not any one leader. The prime minister is simply whoever is the majority party leader in the House of Representatives. There's really not a lot of prestige in being PM.
And in principle, parliamentary majorities stay in power even if the leadership changes, so they are as stable as a system as presidential ones (the institution where most power is concentrated remains).
This, also.