Given that wages in India and other places are clearly artificially depressed, or people wouldn't want to come to the US, I don't think it's obvious that the multinationals do want open borders. I think it's in the interest of workers though.
I would also add that it's wrong to assume that just because an immigrant was hired for a highly skilled job that automatically means there is a native somewhere with an equivalent skillset and able to do the job as well. It boggles the mind how some people assume that somehow every single top expert in the field happens to live in the same city/state/country where a job opening is published.
The labor market is not national or local for a multinational company. Hence, as I wrote, if people are being underpaid in some countries, it is in a multinational's interest to keep them in those countries to exploit, and not let them immigrate to where they could make more money.
Average wages for immigrants is lower than the non-immigrant average in almost all societies.
Because we are in high-tech, we think about 'Google' bringing in great talent, which is good ...
But for most, it's not remotely that.
In Canada, in the Oil Sands, they push for migration and the term they use is 'high labour input cost'. Literally high wages.
So yes, in the long term migration can be good depending on a nations actual need and ability to make use of people, but it's about wages and Supply and Demand there.
It's a similar story everywhere. I don't think anyone, even hardcore nationalists are pushing to get rid of bringing in talented people, the numbers are small. And the issue with H1B for example is not so much the nature of it, but that it was kind of being abused by Infosys etc. in the eyes of some.
"Given that wages in India and other places are clearly artificially depressed, or people wouldn't want to come to the US"
No, this is not any kind of 'artificial depression'. India has a fundamentally different economy than the US. Those differences are not artificial.
Multinationals are almost all in favour of open borders.
They want a) cheap labour and some, good companies need b) high end talent. The later is more rare though.
Every big company I know is 'pro migration' I can't think of a single one that's against it.
Google is more in favour of getting 'highly skilled' people, while most others are in favour of 'bodies' for cheap labour. Companies that are allowed to think long term, like large banks, want migration because 'adding bodies' is the only way most Western economies actually grow. So in Canada, CIBC, BMO, RBC (i.e. big banks) make their $ from mortgages and small business lending - there's no real way for them to grow other than 'more mortgages'. So they push for more bodies as part of national strategy.
Because most political entities, most big business, and a lot of social activists are globalist in nature, it creates a friction with other groups.
This friction is actually a big deal and is reshaping the political landscape in the entire Western world.
It's getting to be less about left/right than it is those with a globalist view and those with a more localist view. 'Nationalists' tend to fall in the later camp.