The context of the current sub-thread is an economic development and wages. So yes, vibrant cities contribute positively to this. As for keeping "cozy" places, that's not a zero-sum game. We can have both.
"Vibrant" is a euphemism. The economic effects of unrestricted mass immigration of unskilled people from third world countries cannot be divorced and analysed separately from the social and cultural effects.
You need only look at any of the places in the US that have already been subject to these waves of illegal invasion, or the various places in Europe that have been flooded with unwanted illegal aliens falsely claiming asylum after travelling through safe countries (with less generous welfare systems) on their journeys to see why people want their countries to prioritise the welfare of their own citizens.
You are talking only about extremes. There is a huge uncovered middle-ground. As for "illegal" immigration, it will always be the case when legal immigration is nearly impossible.