Yes, but I think its a matter of compounding, like in trading. First you make robots, who make more robots, and then those robots can make the stuff we need. Of course you still need lots of jobs to put it all together, monitor it, and all that jazz, but even getting rid of the bottom 10% of jobs will be incredibly destabilizing. These are the jobs most immigrants would typically take when resettling into a new country.
I think when peak labour hits, which is very close I believe, then its all down hill from there. Just today I read about how the insurance industry will go into a downturn because autonomous cars will require so much less insurance since accidents will drop by 90%. Every industry is going to be hit. There are also multiple examples of fast food restaurants operating with less and less employees, which, once again, are jobs taken by immigrants. Even a 5 year time line is I think problematic. By then, autonomous cars along with autonomous trucks might be online. Then we just have to watch where the chips fall.
The housing crisis came about because what, 7% of the people defaulted on their loans and those investments went bust? So imagine just a few of these low skill sectors going bust, and same thing with the knock-on effect.