Naturalization should only involve fulfilment of legal requirements which is the bucket all of what you said falls in.I never said citizenship should be excluded to a birth right. I stated "I view citizenship as a whole lot more than just a piece of paper in the end." Common definitions discuss rights and responsibilities. Without getting all law and order about it, responsibilities would include following the processes set forth by the country you want to make your new home.
In the end, naturalization should involve more than crossing a border and being automatically cued up for a piece a paper as you describe it. I know a little about how naturalization works in the U.S. when the rules are followed. I don't know how Canada does it, but Canada doesn't have a border problem either.
Which is why I recommended a path to citizenship for illegal immigrants who have been here for many years with ties to the land.
As far as the immigrant is concerned citizenship is indeed a passport.
Which is a piece of paper.