There are plenty of ways in the which immigration makes the pay cut less problematic.
1) You have a deathtimer that if you dont get the paperwork in time, or the lottery, or whatever, you can be kicked out of the country.
2) You dont enjoy the same liberties as nationals
3) you dont qualify to multiple benefits that make financials tennable (i.e. medicare taxes, college subsidies, etc)
4) Up until recently, spouses of H1B workers could not work. That is somethign that was added in 2015, and that in this administration its been talked about removing, meaning 50k people lose their legal right to a job.
5) Inherent social issues of the popular cities. San Francisco and Seattle have very high homeless populations.
So yes, there's plenty of reasons to take a pay cut, one way or the other.