I overall agree but I do think the QB position is different than other positions on the team. I tend to think that a QB that does adapt to the culture and learns to love the city he plays in, especially when you are talking about a smaller market like New Orleans, Green Bay, etc., is likely a better leader for the team and is likely going to care more than a player that is literally just here because he is getting paid. Doesn't mean he has to live here 100% of the time, but it helps to truly love and get the city where you play. For instance, Brees spent much of the offseason living in San Diego, but he clearly loved and got New Orleans.
That's doesn't obligate Carr to do so and I don't blame him if he doesn't get or love New Orleans having grown up in California and played out West for his entire football career, but at the same point maybe if he doesn't love New Orleans and doesn't embrace the culture, maybe he isn't the right QB for New Orleans?