Even if there were no legal or immigration costs (which there definitely is), it seems to me they could easily do the same by getting someone from a less prosperous part of the US and moving them to, say, CA. I'm sure this happens all the time.
I would also imagine it's a lot easier to convince an employee to "go the extra mile" when you're dangling their ability to remain in the country over their head, especially if they're also applying for citizenship.
It's also not just about saving money. Modern day corporations (and probably old fashioned ones) are basically extortion pyramids. The entire livelihood of everybody with employees at a corporation depends on having complete control over their subordinates. Why would you hire someone that can quit when you piss them off. Corps hire people for management jobs on visa as well. Its all about control. The thought is you're nothing if you don't have people under control. It's sad that corporations work that way, but that doesn't change the fact that they do.
You are correct that outside IT, hiring decisions rely heavily on the community. Within most serious IT firms, which definitively include Infosys and Tata, hiring is roughly as meritocratic as it is in the west. That's due to simple market forces - your community is simply not big enough or smart enough that you can hire exclusively from within it.
("Community" refers to a narrow slice of your ethnic group, e.g. Parsis, Gujus or Conkanis.)
This logic seems wrong: if a person moves from somewhere to CA, they should now be paid a CA-level salary. Consider that at any point they can quit, and to every other employer they will look like a regular CA job market participant, so the other employers would offer them a CA-level salary. So you can't, in fact, hire someone from outside CA and have them work in CA at a low salary: they would just quickly move to a similar but higher-paid job.
This logic breaks down with visas that restrict your choice of employers. If your freedom to pick your employer is taken away, then your logic is correct: it would be possible to hire someone in CA at a low salary, without them immediately switching jobs, because they are forbidden from doing that.
The 20% premium that the company collects on the salary is (at least partially) a consequence of this lack of employee's freedom in the labour market. Without this restriction you would expect skill-adjusted salaries to be equal for visa and non-visa employees. It's not even anything to do with immigration per se, just this type of visa.
It drives down wages across the industry by increasing unemployed labor supply. It's a lever to put downward pressure on wages in a macroeconomic sense.
They're probably saving a lot more than 15-20%.
I understand this argument is often used to claim that it isn't about wages, it's about availability of someone, anyone to hire. But at what rate?
Suppose you say that you can't hire a developer with a particular in demand skill set. You've posted at what you've determined to be "market rate" for the position, or maybe a bit higher You pick up the phone and call various highly regarded developers at google, apple, and Facebook and say "what would it take to get you to quit your job, this moment, and come work for my company?"
My guess is that the difference between the "market rate" the company is offering and the rate they'd pay if they were prepared to do what it takes to get that engineer to leave google is a lot greater than 15-20%. I wouldn't be surprised if they'd have to double the offer.
The Indian employees at TCS and Infosys are ready to work long hours and obediently carry out orders without questioning anything, which sometimes helps.