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That is kind of a contrived scenario.As is the "boundless immigration open for all" scenario to begin with. But given that, what could happen? That's one possible answer.
>For starters, what is the motivation for these Muslims to migrate to America or western Europe if their goal is to create an Islamic state?*
Expanding islam to other places is part of the historical identity of islamism. Might not be on the goals of peaceful laymen, but it's very much a core tenet of more devout believers (not talking about militants either).
But an even more obvious answer, at the layman level, would be they'd migrate to take advantage of the wealth, infrastructure, opportunities etc. The making an islamic state can always come second. After you have those, why not change the laws and customs to your preference too? Especially if you are a large enough subset of the population?
>If your argument is that they want access to our economic prosperity, the act of converting our government would destroy the very system that created it.
That's how you see it. They don't necessarily see it that way, and I don't believe that it is that way in reality either. You can create prosperity under very many systems. I don't believe the US has some unique model for how a wealthy state must be run. We have from far more socialist economies that do quite well (e.g. nordic countries), to light totalitarian states that do great (Singapore), to "communist" single party states that are rising fast (China).
>If your argument is that they are dicks that only care about creating a tyranny of the majority to "punish" others
You call it "punishing" others and "being dicks".
As they see it, it's just putting others on the right track and being moral and just (according to their beliefs). Puritanical western societies have not done less (e.g. with the Inquisition and similar establishments).
>My experience with immigrants is that they generally want to be able to maintain some semblance of their culture in their new homes, but they generally aren't interested in foisting that culture on others.
That's because their small numbers make them humble and appreciative of where they have been received. When there was mass immigration (e.g. when the English and such religious nuts migrated to the US) they very much forced their religion and customs on others (native americans for one: https://en.wikipedia.org/wiki/American_Indian_boarding_schoo... ), but also WASPs as the dominant majority group over Jews, Irish, Italians, Chinese, etc.