You can think of the Canadian approach as a variant of an English or Scottish Name & Arms clause, minus the Name
It is, as Joe notes, an approach to rendering armorial inheritance gender-neutral - not the approach I would have chosen, but somehow my royal appointment as Governor-General seems to have been lost in the mail.
As for flocks of armigerous Canadians migrating to England, that's not the immigration crisis that's been in the news lately; though apparently Lyon has denied matriculation of Canadian arms in Scotland because the lack of link between Name and Arms is not compatible with the nature of arms in Scottish law. (Others can confirm, clarify, or correct as necessary.). All of which is great spectator sport from Baja BC!
For the record, the Canadian approach is not the only inevitable way to reconcile heraldically inheritance with gender equality, so long as we remember that Heraldry is a tool to signify identity - that is, identity is the dog, Heraldry is the tail. In the English-speaking world, at least, the primary social and legal identifier of family has been & still is the surname; and in modern times at least, the choice of surname, and therefore of primary family identity, is a personal choice. Traditionally, that has been the father's name before marriage and then the husband's; but nowadays, children may be given either or both parents' name; and married couples may bear either or both surnames. Most families still follow the traditional pattern, but that is by choice, not legal or societal mandate.
That's the situation nowadays, before reaching the question of which arms to bear, since that choice is secondary to choice of name. If the function of arms is identity, then use whichever arms actually reflect the identity - the surname - that each individual or family has chosen to assume and bear. To my mind, bearing the coat of arms tied to one side of one's family while bearing the surname of a different side of the family fundamentally fails the basic purpose of arms as an accurate identifier of who and what the bearer us, both legally and socially. There are other ways to signify family connections of differing surnames - impalement, quartering, and composition come to mind - which allow for the emotional connections without sacrificing the connection between Name and Arms which give the display meaning as an identifier.