Because you're a South Asian?

Educate the next generations and help a country become a first world country.

Cheaper cost of living (probably)

Some people actually like to live in their own country, and I do not think it should be considered strange or problematic.

@Greg, Low-quality healthcare, weak transportation, corruption in the system, etc., are some issues.

@Prof.SantaClaus That sounds like a great cause. Is it really a rationale on an individual level, though?

@user366312 Those (poor healthcare, transportation, corruption) are not academia-specific motivations. Then the question simplifies to "Why does anyone want to work in South Asia?", which is probably off-topic.

There are a wide range of professional and especially personal reasons, some of which are choices (e.g. staying near family), some of which are not (e.g. being unable to get a visa), for why one would work in one country instead of another.

I also cannot give you a reason why anyone would would want to work in academia in developed countries.

If you want to work twice as hard for half the pay it is probably a good idea to do so in a place where the cost of living is low.

You help them develop more quickly.

I will make this comment an answer when I have the sources to back this up. But I think in the case of India, the healthcare costs are not something that you might have to worry about a lot, atleast compared to the US, if I understand right. The doctors are available well in the private hospitals, and even though the costs are high (relative to the public hospitals), these hospitals do have quite advanced technology and great doctors and it should be quite affordable enough for an academic professor in India.

It might be cheaper in public hospitals, and the doctors ARE well qualified, but the infrastructure and technology might not be as sophisticated (and is sometimes rather poor).

And another reason I can think of is, lower cost of living and that the cost of getting household help or childcare help is much lower and affordable. The latter is not something to boast about, as it mainly comes from the huge income inequality in India, and I definitely hope the situation improves, but then I have heard people talking about this as part of the reasons they have shifted back to India.

It helps if you have a patriotic feeling toward the target country, and making conditions in that country better has a large inherent value to the concerned individual. Not everything is money (though you need to eat!)

I've been involved in an engineering education project in an LMIC, and have some possibly relevant observations, but not necessarily directly relevant. I can try to frame the experience in an answer, if you're interested.

Are you asking from the perspective of someone in a developing country choosing between academia and industry? Or someone who wants to work in academia and deciding whether to go to a developing country?

Are you looking for an answer more sophisticated than "Because they may have family and friends there, and/or may prefer to work in their native language, and/or not be subjected to casual racism both in professional life and outside."?

It's not as straightforward as you make it sound. When I finished my PhD I applied to postdocs in Europe but they were all quite boring and working on things I didn't want to do, whereas a project came up at KAUST which I actually wanted to work on (although technically it is in Saudi Arabia which is considered a developing country). In reality working at KAUST is almost indistinguishable from working in a European university with first-rate healthcare apart from heat and cultural differences.

@user366312 weak public transportation you mean like what is the case in the US with every city except NY?

The assumptions in the question and some of the comments are somewhat ethnocentric/nationalistic/offensive.