1. India has a lot of beautiful and varied landscapes. There are mountains, lakes, forests , beautiful beaches , backwaters. I cannot do justice to the amazing places I have seen.
2. Almost everyone speaks English. In some places, to make the tourists feel more comfortable people have learned Hebrew, French and German.
3. Things are indeed cheap.
More controversially, I have also been told by travelers that the other reason India remains so popular is that drugs are incredibly easy to score, especially in some tourist spots.
The other thing is that a lot of tourists do not keep travelling among hordes of poor people. If they go to Goa, they hit the beaches directly where they meet other tourists and other people trying to sell exotic crap. If they go to the mountains they live surrounded by other tourists.
It is hard to describe the feeling visiting some of these places, perhaps it's a bit like visiting Delphi or the Acropolis. My favorite was the Red Fort near the Taj Mahal.
It's a lot easier to describe the bad things about India than the good things.
I too have a very low opinion of India like you do. I have often said food and yoga are the only great things to historically come out of India and a few good mathematicians of course. So food alone is one reason to visit!
The others here have mentioned about the geographical beauty of India. Skiing in the Himalayas alone is worth it.
I was born in India but moved away at a very young age. I did go back from time to time. Like you, I too think Indian culture is old and full of ignorance. It is biting them in the ass. My comment history will attest to that. But then again, what developed nation wasn't? At some point the church prevailed in Germania too. But this is changing, albeit at a slow pace. Why? Indian values have been traditionally been placed on peace/ cowardice ;). They never had a deranged lunatic who propelled them into the scientific age with a war based economy killing half of his own population. They never had genetic cleansing of population. So any change into the scientific, modern age is going to happen at a very slow pace. Unless of course they go to war with China and their existence is threatened. I guess you can see what I'm getting at. Spirituality. There's a fundamental divide in east-west spirituality and its a lot more deeper than you think. It's enlightening to visit these places. Please do read autobiography of a yogi or anything by vivekananda if you go on such a trip. It's not just mindless, non-scientific drivel. You'll see a fundamental difference from Nietzsche.
Next, history. India is home to the oldest known civilization in the world, the indus valley civilization. So you can imagine how rich the history is. And needless to say, I'd imagine you know the importance of visting historical sites, especially say Auschwitz in your country. There is some stuff we never want to repeat. Oh and I couldn't help but type this, you can take a train in India without fear! I kid, I kid.
Why do poor people like traveling to Hollywood?
The crimes and experiences as highlighted in this article however are completely inexcusable.
To me it was obvious as soon as I got there (mumbai, then delhi, jaipur and agra) that there was grinding poverty, little modern infrastructure, little to no sanitation, mass corruption, inequality unlike anything I'd seen before, incredible overcrowding... Quite horrible.