There's a lot of people who would conceivably get caught on the wrong side of that.

My policy would be "people that are already in the process of getting a visa are allowed to live in the country if at the end of the process they are granted it"

Who gets to define whether a change is for the better? Or if "better" is good enough?

I hate to bring up the same example twice but so be it. Muslims as I am sure you know, follow a "holy book" that is essentially their life long law. That book says that women should be treated as 2nd class citizens something that isn't acceptable in western countries. If overtime more followed the muslim way (unlikely but anyways) wouldn't it be a threat to western values?

I can tell you from experience that at least in the US, the process is already VERY concerned with assimilation.

Let's get away from the US for a second. Countries in the Baltics or the Balkans or Asia where their neighbours want parts of their land and people moving to a neighbouring country do it out of need but in fact downright hate the country they are moving in and would like to change it to their liking. Recent examples of this would be Russia annexing Ukraine, or the Albanians making Kosovo independent from its host country Serbia. And many other conflicts that I'm sure Wikipedia has a huge list of.