Your direction of thoughts is right. But this particular rule is completely opposite to your conclusions. Ж and Ш are "hard" consonants so by ear И after them always sounds like Ы. But the rule tells us to write И instead of Ы. This rule of Russian spelling does not make any sense that's why every first-grader knows it.
Well, "propiska" in Russia is a dying institution, actually no one is really interested where your "propiska" is. In recent past there were some troubles finding job without "propiska" in region, but it passed. We have fees for people, who do live outside of their "propiska" region and do not tell government where they live, but these fees applied to people extremely rarely.
About "traitor" thing - well, usually everybody understand that there are better places to live than small city in Siberia. People move very often. For example, after school 20% of my classmates moved outside of Siberia and almost everybody left my small city and moved to a bigger one. I were born in Siberia and moved to Saint-Petersburg a year ago -- no one called me a traitor. They even come as guests, stay in my apartment and sometimes think about moving too.
I've met a couple of people from Norilsk - they are glad they moved out, but proud of the place of their origin. Which I consider pretty healthy position.