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There is no law of nature that demands this. These rules were written by people. They can be changed and bent by people as well.
You're gonna be seeing a lot of changes very soon. Don't go thinking the neoliberal status quo is some default state of the world. The US is fascist now.
This still seems wildly unlikely for so many reasons. Canada needs new trade partners and at this point some defense guarantees, but joining the EU is a long shot.
And it's one that will take too long to have any bearing on current challenges anyway.
That said, Dumpster's moves are mostly ridiculous because he's trying to speed run something that was coming eventually. He's just skipping the rather slow but crucial propaganda step to manufacture consent, and trying to de-integrate our economies at self-immolating speed.
I think it might be a good idea to explore membership in the Schengen Area and/or European Free Trade Association, but full EU membership is more trouble than it's worth and Eurozone membership (giving up our currency) carries serious drawbacks alongside benefits I wouldn't expect to fully realize with our geographic separation.
We can and should be looking for better economic integration as part of our trade diversification. But we also need to preserve our own internal autonomy and power, and shouldn't be expecting any meaningful protection from across the pond. I mean maybe fellow Commonwealth states will militarily support us, but not likely the EU, and definitely not within a decade. We're not like Ukraine who sit between them and a hostile neighboring state, softening the latter without costing EU lives.
I like the idea I do but I think the CANZUK is more likely the four countries share so much more than we do with the EU. Only problem I have with it is we would still have the royal family on our coins.