If we're going to remove that capability from the GG, it has to land somewhere, we can't just not have it. In that case we should have a process whereby the PM is selected by a majority vote in Parliament. That way if an opposition leader commands support of the House, the House can make the appointment.I theory yes. In fact not a chance. The GG will not act simply upon a request of another minority party leader to form a government. The office of GG today is largely symbolic. The first time the GG acts as if he/she has real authority from the the Crown would also be the last.
Currently it's left to the GG to do things like that, and the GG is supposed to go around and consult with people. If you remove the power from the GG it can't just be removed completely--the GG has to be replaced, not simply snuffed. An alternative would be go keep the post of GG, with all the usual reserve powers, but remove the claim that power flows from the Queen. In that case the GG should be appointed by a super majority in Parliament and the Senate, a sort of bicameral speaker, and derive their authority that way instead.
In fact I think the GG plays a crucial role in Canadian democracy. One that does not require exercise of power more than once every hundred years or so, but when exercised, can mean the difference between a democratic and a non-democratic society.
Specifically I see the GG as the last line of defense against a dictatorial Prime Minister who refuses to follow custom and tradition and attempts to usurp more power than is due to a PM.