Yes.
This is a longer discussion perhaps, but I would assert that we need more than just coordination. This is a national imperative, and there's no constitutional barrier to preventing leadership on this file from the national level.
On the issue of international students, both in terms of Canadian students studying abroad and foreign students studying here, for a long time Australia was attracting more students from China, but I believe last year Australia started attracting more students from Mexico than Canada. Is it a question of resources, or is the Australian government just more focused on this in terms of the amount of investment they're making? Would it be a good idea to develop some sort of national or internationally recognized scholarship program aimed at attracting the best and brightest to Canada, something with a branding capacity of, say, a Fulbright or a Rhodes scholarship?