Migration is a policy issue, not some natural force like osmosis. It's entirely irrelevant why migrants want to come, when you have an existing population that is being harmed by migration policy.

It's simply that the wealthy benifit from increasing labour supply; this is the "enrichment" you get. Not an improvement in culture or conditions, an increase in wealth concentration.

It's entirely reasonable for a citizen in an English speaking nation to complain about other languages becoming common, as it is direct evidence of the migration policy that is doing them harm.