It’s not clear at all to me that the Governor General cannot be called Canada’s head of state in at least some contexts. (Monarchists, please direct your hate mail to my correspondence secretary, Nigel, who much prefers to read letters written in fountain pen and sealed with wax.)
Not that I’m claiming true expertise in matters vice-regal. All I know for sure about Rideau Hall is that it is customary when cricket is being played on the grounds to begin tea with cucumber sandwiches, whilst watercress is much preferred on croquet afternoons.
But be that as it may, in 1947, King George VI signed so-called “letters patent,” which gave the Canadian GG the main duties of a ceremonial head of state. In Governor General Roland Michener’s time, GGs traveling abroad on Canada’s behalf began to be greeted by foreign governments as Canadian head of state. (Read about it here, under the interesting heading “a Governor General as Head of State…”)
So our GG carries out the duties of a ceremonial head of state. And she is treated like a ceremonial head of state. If it walks like a duck, and quacks like a duck, and wears a lot of gold brocade on its epaulets…