India has only become a natural US ally fairly recently... And largely due to the 'frenemy' status that the US has with China. (Which in itself is a consequence of the 'frenemy' status that the USSR had with China... It's turtles all the way down.)
Through much of the Cold War, US-India relationships were very, very cool. Instead, they had good relations with Russia, while the US had good relations with Pakistan.
There's nothing 'natural' about nation-state alignment. It's all political, and politics is capricious.
However, I claim that it can be expected to be sufficiently true for the next several decades, to the point that continued rapid development of India should not only be something the US doesn't have a problem with, it should be an explicit strategic goal of 21st century US foreign policy. It's not every day that self-interest and humanitarianism align so well on a matter of such importance; it would be a pity if the opportunity was not taken.
What has made the past 50 years so peaceful (amongst the big powers, at least) is that nations that share values have aligned. France and Germany and the US and Australia share a philosophy of governance, not just a short term realpolitik goal. (Of course sharing a language helps too: Canada, UK, US, Aus, NZ are tight for that reason in good part)
But I think the emphasis on values is unfortunately not true. The parent overlooks all the right-wing dictatorships that the U.S. allied with, from Indonesia under Suharto to Iran (under the Shah) to Iraq under Saddam Hussein (when Iran turned against the US) in the 1980s to Chile under Pinochet to the junta in Greece to Saudi Arabia to Egypt to Mobutu in Zaire/Congo to Central American dictators to many more on every continent.
And today, right-wing dictatorships are arising among NATO allies, but I haven't heard a word about ejecting them from the alliance.
Immigration is, I believe, a human right. It's liberty - liberty to travel, to make the most of yourself, and it's opportunity. People should be free to make the most of themselves. It's also economic freedom, which generally yields more productive economies for all.
For practical reasons, mostly to prevent the economic shocks of mass migrations, it needs to be somewhat limited and controlled. But I want the poorest, most oppressed people coming to my country; they are the ones who need freedom the most - the most marginal social and economic gain. I'm completely confident that they and their children will thrive and make my country better. And for practical and moral reasons, I'd like more diversity; the sooner we can do away with the dominance of any ethnic group, the sooner we can be rid of their BS bigotry, which is a drain on us all. (Imagine, for a moment, the world without bigots - so many problems solved.)
A corollary is that you should be allowed to join organizations that want you.
But entry to any organization, regardless of whether they want you or not? In a world where Google has to hire everyone who applies, or Stanford has to admit everyone, or families have to house and feed anyone who shows up at their doorstep even when they don't want to, you no longer have a Google or a Stanford or a family functioning anywhere close to its current level. "Entry to anywhere as a human right" is an idea which may be initially attractive due to its simplicity, but the only people I know who stick with it after further thought appear more interested in harming groups of people they don't like than trying to lift up everyone.
And as a practical matter, for all of its flaws, the US has nevertheless done more than any other country over the last 7 decades to enforce a right of exit across most of the globe. A more diverse and stronger US would be an improvement, yes, and I'm pretty sure Canada/Australia-style immigration policy will get us there. But there are ways to become more diverse and weaker, too; and importantly, in that world, bigotry is even further from being solved, because the probable leading superpower is a more bigoted, monoracial China. (In contrast, when the City College of New York ceased to be a top-tier institution, the damage was fortunately limited to just itself; other top universities had ended anti-Jewish admissions practices some years earlier.) You seem completely blind to this danger.
It is straightforward to verify that they don't stop holding at nation-scale. A good place to start is Lee Kuan Yew, who's both one of the only leaders in history to preside over the entire transition from Third World to First World for millions of people, and an architect of what's currently the most open immigration policy among Chinese-majority states. Singapore is a multicultural place whose government is widely acknowledged to have one of the best technocratic track records in the world, and they spent considerable effort on trying to get immigration policy right, iterating through alternatives while deliberately taking a popularity hit; what were their conclusions?
Or what are the odds, under your stated worldview, that two of the closest things to actual open borders existing in 2018 are (i) the Norwegian archipelago of Svalbard, which lets almost anyone stay as long as they can support themselves ...but ranges from 74 to 81 degrees N latitude, and (ii) the United Arab Emirates, which has more than five times as many expats as actual citizens, the largest number from India ...but ruthlessly maintains a two-tiered society, where even people who were born in the UAE and have lived there their entire lives are exceedingly unlikely to be granted citizenship unless they are Arab?
Contrary to claims that nothing like open borders has ever been tried, the existence of cases like this make it abundantly clear that this area of policy space has already been subject to substantial exploration. And every surviving result has an obvious and unusual force that does something similar to what traditional immigration controls accomplish in most countries, such as Svalbard's -40C winters. This is, to put it mildly, not a likely result if traditional immigration controls no longer have a useful function.
The boundaries of Apple, Microsoft, Google, Amazon, etc. are "arbitrary [and] invisible" to some extent, and obviously drawn by the powerful. But "the current set of lines are arbitrary and clearly not the only possible solution" does not imply that "no lines is a better solution"; indeed, the latter has only been empirically true when there are preexisting strong and stable force(s) which perform enough of the function of explicit admission criteria to render the latter unnecessary. In real life, you find formerly-exceptional institutions which quickly and irreversibly declined to a lower level after switching to the open admissions policy that your phrasing advocates for (consider the City College of New York in the 30s-60s vs. afterward).
Instead, the most impressive results in both hiring and immigration policy have combined race/nation-blindness with a distinct lack of blindness to other criteria which really do matter. You cannot do the latter (and perhaps more importantly, properly incentivize cultivation of the relevant personal and institutional qualities across the world) without maintaining some "arbitrary, invisible" lines across at least a multi-decade timescale.
So, more immigration and education of foreign students? I'm totally fine with that, for both national and universalist reasons. (This is particularly clear for India, which is a natural US ally. None of the 'frenemy' complications we have with China; I WANT Indians to 'steal' more of our tech!) But only on the right terms, which are not being offered by anyone using the language you're currently using in the second half of your first sentence. I suggest that you explicitly distance yourself from those people if you want the rest of your comment to be heeded by anyone outside your tribe.