>C.f. the hardline anti-immigration voter who thinks that the guy who mows their lawn obviously won't be included in the crackdowns.

huh, that's pretty bizarre, at least here in Australia (where in recent years immigration has exploded to 2x ~ 3x that of the USA), all the anti-immigration voters are sincerely hoping the guy who mows their lawn grew up across town where his wife's sister now lives.

the crackdowns are for the economic migrants just taking a lifestyle arbitrage

ultimately, immigration into large developed nations is an act of altruism, which, like most things in life, cannot scale indefinitely (much to the chagrin of business owners, women, arts students, etc.) - which is not nice, but is true.