IDP is not a photocopy. It is a very valid document issued by your country authorities as well. The only difference there is that:
1. it cannot be used in the country that has issued - there you need a local driving licence.
2. it is valid much shorter from the day it was issued (1 or 2 years depending under which convention was it issued).
3. it may or may not contain language of the country that has issued it. However there is list of languages in which it has to be written (that is why is it mostly a small booklet and not just a simple card).
Canada is using Geneva convention and as such are accepting IDP issued according to this convention.
Would there be no grace period in order to get Canadian driving licence for newcomers, it would be heavily unfair for all those that cannot simply exchange it. That is there is the time given during which you can use your IDP while getting local driving licence.
https://travel.gc.ca/travelling/documents/international-driving-permit
My real experience:
Nobody in the rental company was asking for my local driving licence. All I needed was a proper international driving licence (Geneva convention), to be able to rent the car for the driving test.
And my own (now expired) IDP states following:
this ID is valid in all countries of this convention (1949 Geneva) except of the country that has issued it. It is valid for 1 year from the day it was issued and it gives right to drive motor vehicles of all groups that are confirmed by this ID.
There is nothing stated that I have to have my local driving licence with me as well when using that valid IDP.
From Geneva convention (Canada signed this one, so it is bound by its rules):
Article 24
1. Each Contracting State shall allow any driver admitted to its territory who fulfils the conditions which are set out in Annex 8 and who holds a valid driving permit issued to him, after he has given proof of his competence, by the competent authority of another Contracting State or subdivision thereof, or by an Association duly empowered by such authority, to drive on its roads without further examination motor vehicles of the category or categories defined in Annexes 9 and 10 for which the permit has been issued.
2. A Contracting State may however require that any driver admitted to its territory shall carry an international driving permit conforming to the model contained in Annex 10, especially in the case of a driver coming from a country where a domestic driving permit is not required or where the domestic permit issued to him does not conform to the model contained in Annex 9.
3. The international driving permit shall, after the driver has given proof of his competence, be delivered by the competent authority of a Contracting State or subdivision thereof, or by a duly authorised Association, and sealed or stamped by such authority or Association. The holder shall be entitled to drive in all Contracting States without further examination motor vehicles coming within the categories for which the permit has been issued.
4. The right to use the domestic as well as the international driving permit may be refused if it is evident that the conditions of issue are no longer fulfilled.
As you can see from point 1 and point 3 makes local driving licence which already is according to Geneva convention and IDP an equal document
https://en.wikisource.org/wiki/Geneva_Convention_on_Road_Traffic#CHAPTER_V._DRIVERS_OF_MOTOR_VEHICLES_IN_INTERNATIONAL_TRAFFIC