I agree that "India and the US are natural allies" is not the kind of statement that has a multi-century shelf life, for the reasons you describe.
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.
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.