Importing massive amounts of unskilled labor only depresses wages and, combined with NIMBY, creates a massive housing bubble thanks to artificial shortages.
In Australia's case, it also suffers from a disproportionate brain drain of highly educated professionals since local firms simply won't compete for talent.
edit: I think the "quality" argument is overrated. Not all immigrants do ground-breaking research or start billion-dollar companies. When it comes to economic activity, quantity has a quality of its own (apologies to J. Stalin). A city/state/country with the economic activity of an extra 20% population of mediocre, healthy, tax-paying, car-buying, mortgage-paying, burger-eating blue and white-collar immigrants is better off than one without.
Except for categories where there's an extremely high burden of proof for extraordinary abilities, it's simply someone's ability to get a job no American is qualified to take (and be so in demand that it commands a salary in the top percentiles for the profession).
So the market takes care of the selection.
Not exactly, its someone's ability to get a job that their employer cannot find a more qualified candidate after advertising the job in the local newspaper for 6 months including at least two separate Sundays.
This is obviously my idle speculation, and I think the UK voters would never be allowed to vote on such an opportunity anyway. Still, I think if it happened it'd be great for everyone.
I feel like if there was a referendum, the UK's population would happily dump their monarchy in exchange for US statehood. There's a lot of commonality with their democracy, language, skepticism of foreign immigration, embrace of capitalism, etc.
It would also be a pretty solid strategic move to bring the US closer to Europe as a hedge against the Russian ambitions laid out in their Foundations of Geopolitics playbook.