The legal ones, perhaps.
What you describe is the theoretical system for immigration we had before the illegals became the problem. Mexico and Latin America have always had numerical preferences and I have absolutely no problem with that. As a matter of fact, I am one of those.
Your (optimistic) blanket assesment of the illegal mindset, however, is contradicted in my real life experience. Right here. Right now. Where I am living.
Illegals can't be integrated at all which is why they don't have an "integration-oriented" mindset. Make them legal in any way and that would change.
Yep, I'm in L.A. too, I've seen it all myself. It could be that I'm too optimistic, but maybe that is a better guide than pessimism.