Indian here. Not true, most of us love our country. And people do love to go back. Relocation in general is tough, once you have a family and kids going to school, its really tough to go back
I am not going to blame you are anyone else trying to make it, but I find it quite hypocritical that Indian publications glorify people who have pretty much left the country for good.
Has the West not done the same? Who was Mother Teresa? When she adopted India as her home, leaving her birthplace for good, to help the distressed, did the West not glorify her as a "savior" and elevate her status to a "Saint"? Heck even after her death, lots of Western publications still continue to praise her work (and rightfully so). Should we call the West hypocritical then?
Just because Sundar Pichai left India for good does not make him any less Indian. At the same time, he is also not a celebrity.
If you bother to look at other articles published by the same publications you referred to, you'll notice that they praise a lot of other, more powerful Indian entrepreneurs as well. Sundar Pichai is not even on the same plane as those of Tatas, Birlas, Kirloskars etc. These are the local celebrities (household names if you will). Not Sundar Pichai. Go ask any Indian about Tata and s/he will tell you everything they know. Then ask about Sundar Pichai. That is when you'll understand who is the real celebrity in India.
I have seen from most of my friends in US, their love for India is mainly remitting dollars there and talking about politics/cricket/cinema.
Indian schools are very different. Indian education (up to but not including college) is very different. While top IB schools and whatnot (which are super expensive and may not be affordable even if you have earned money in the States -- besides, you will be earning less money now) exist and are closer to the Western model of education, most likely you will be in something less expensive. There is an enormous focus on rote learning. There is a very high competitive attitude. These things are _very hard_ to adjust to. Rote learning especially; that's not taught in the US, and is a very hard skill to pick up at a later age. This is not something that can be trivially brushed away.
(The reverse is true too; I know Indian kids who have had a hard time when moving to the West.)
And really, schools are often why people avoid moving from state to state in a country, forget moving to another country altogether. Its generally about not wanting to uproot your family's life. Schooling is a big part of that.
Nobody's saying schools don't exist in India.
Source: I'm an Indian-American who came back to India and had to switch schools. I know many other families who have done this.
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Edit: Some other things that I missed:
The school year is different. Furthermore, many schools (at least in Mumbai) start the year in feb-apr before summer vacation.
Languages. Depending on your location and the grade you're in, you may have to learn one or two languages other than English. If the child is very young this is okay, but you can't expect older kids to pick up the new language and get to the level of proficiency expected at that age. Most Indian-American kids do speak one Indic language, but not necessarily to the degree of proficiency required. They may not speak Hindi at all.
Many exam boards allow for some flexibility with choosing a different language, like French. But most schools won't have the faculty for that.
In my case there was exactly one school in all of Mumbai where I would not have had to have Hindi as a subject AND would not have had to sit out a year of school (this was after leaving my American school a few months early -- they were okay with that because I had good grades. Imagine the situation people would be in if they didn't have the grades necessary to be able to leave school early.)
I actually still started after the school year was underway, but fortunately this school was okay with that. Didn't help the transition between education systems though.