This is part of the point: this aspect of immigration labor would ironically disappear if it was easier to get into this country. The fact that its hard to get in and get a job is precisely what creates the imbalance of power in negotiation and further leads to a sense of indebtedness.
BTW, this also negatively affects startups. I've been in situations where its difficult to poach someone because of their visa situation (they don't know how easy or hard it is to transfer, they feel indebted, etc etc), and additionally, its way easier for large corporations to go through the paperwork to hire outside talent than a small startup thats just 3 founders. Regulation, as usual, creates all sorts of strange counter-intuitive incentives and imbalances.
If companies could just hire whomever they wanted, then sure, you might be competing directly with someone from india, but you'd also be on a more equal footing because that guy from india would have the same mobility to other jobs that you do, and thus would not be so desirable for his "capturability". Not to mention the fact that whether you like it or not you'll eventually all be competing anyways: at some point it just becomes easier to open offices there and then there's just no job here period.