Yes. We don't them any more; they are just a useless relic of our past.
BTW, parliamentary republic unusually have a president instead of a monarch. The German Chancellor is a Prime Minister; there is a German president as head of state.
I see a Canadian president with subordinate provincial governors replacing the current system.
Oops, got my terms wrong.
Still, I like the term Governor General for the HoS over President. I wouldn't give the GG such a level of power that most Presidents have anyway.