Having PMs elected by MPs means that it is harder for a single rabble rousing politician to sweep to power and distort the use of, say, the military.
Having Governers General appointed by PMs, and confirmed by the monarch, means that someone outside of politics (usually a well respected figure like a university president or astronaut) holds the final red line about whether or not an election must be called. Since it's via appointment, the monarch doesn't bear the brunt of the public rage for it. And since the monarch must confirm the GG it means that the position can't be stuffed with an obvious political hack.
It jives better than it sounds it would jive. It's like checks and balances with as many arguments and gridlock.
As an aside, I feel the same way about the Notwithstanding Clause[0] of the Canadian Constitution. It's a useful tool to diffuse hard issues that can't be used against the public to stop them from voting or speaking and since it automatically expires after a short, preset time the power is ultimately in the hands of the electorate.
[0] https://en.wikipedia.org/wiki/Section_33_of_the_Canadian_Cha...