even then calling it an organization is not really that accurate
It is an organization, you can go work for the NATO directly. They are headquartered in Brussels.
That said, military intervention on behalf of NATO works as you described, but there would be an obligation to help Canada in your example if the war would spread to its home soil. That said, the help obligation is literally worded "as they deem necessary", so they could pretend that no large-scale intervention is necessary.
This is essentially what the Ukraine EU accession talks are about. The EU is the military alliance they want to join, and it is actually even more protective than the NATO.
So the question isn't stupid, Ukraine actually wants this, the EU is of two minds about it so far.