A steady trickle of immigrants is much better because then it forces cultural integration, especially when the immigrants do not speak English. A flood of immigrants will lead to a nation divided among cultural lines without the possibility of integration because the cultural bubbles will have already been established.
We should focus on helping impoverished nations develop, so people don't have to leave from their birth countries to find comfort.
In the US there's really not any community of non-English speaking citizens, so whatever to your complaints about integration, the kids desperately want to integrate (and the parents usually agree).
And of course the whole thing where foreigners are scary is as much a modern panic as anything. In periods of pretty open immigration, lots of states didn't require citizenship to vote:
https://en.wikipedia.org/wiki/Right_of_foreigners_to_vote_in...
Source? lol
A few thousand people here or there is a laughable threat to whatever culture exists in USA.
But if you look at what I said, I didn't say anything about language spoken at home or primary language or anything like that, I explicitly said community of non-English speaking citizens, which pretty clearly means people that don't speak English anywhere.