If this was the only thing it would have gone offshore more than a decade ago. The reason is hasn't gone offshore is because the results are terrible for a number of reasons, with precious few success stories. It is a tried and failed technique to cut software costs.
Also, even now India exports $100B+ worth of software services to US. It is not as if every project offshored is producing "terrible results".
Paying maximum viable cost for minimum viable output is the type of outsourcing that you're thinking of. India, Eastern Europe, etc is full of smart people capable of doing pretty much anything. Being located in California doesn't give you super-powers.
People are selfish, so I don't blame them for want to close the door and keep the outsiders outside so they can have a bigger share of the pie.
But don't expect to see that happen either, companies nowadays are much more powerful than individuals and they are very nimble, they will go to places where cost is lower, this won't change a bit, it is in their blood.
So to immigrants coming to US, don't really put much hope in spending decades waiting to get permit to not in living in fear of throwing out. Doesn't worth it. And the resentment towards immigrants is worsening everyday, unless you happen to have certain skin tone. So earn your bucks, and save more, when the time comes take your life and skill elsewhere, life is too short to just wait in vain and hope for the best, act swiftly and you will be happier ;)
No H1? No problem, move the function offshore.