Offshoring it hardly new. Take Microsoft for example. They offshored heavily over 20 years ago. Allow more immigration or the jobs will be offshored is an idle threat. Companies have done tons of offshoring and reshored many things after it didn't work out. More or less immigration isn't going to move the need on offshoring much either way.
A key difference is that at least one isn’t competing for limited housing with offshoring. That is the number 1 driver of the affordability crisis atm.
I’m a fan of the YIMBY types but we aren’t building enough annd, until we are, it’s a problem to put more people where we already have little housing!
The post-Covid offshoring is looking quite a bit different though.
Offshoring to India is an idle threat due to radically different work cultures and expectations.
Offshoring to, say Poland or Portugal on the other hand...
Of course it's not new. And of course it never really stopped. But there is a new incentive for execs to give it a much bigger push given all the recent remote work tooling and when they now think a programmer is just monitoring AI output. So why not pay the monitor SE Asian wages rather than US wages.