I very much agree with you. Spreading western values by taking in immigrants is not a bad idea. Even if it doesn't change everyone in the world, it still shows that it is possible for the values to include everyone.

It does assume integration though. If you take in immigrants, but isolate them and/or treat them badly, might it not be that you actually radicalize them further?

(Of course we shouldn't isolate them, but if that effectively ends up happening it has to be considered.)