When I lived in India, I certainly observed that no one there seemed to care about athletics. It's just not in the culture.
I'd regularly go jogging. People would stop and stare - doubly so if I stopped running and did pushups. In my entire time there, I saw perhaps 3-4 Indians running, and considerably more foreigners. The Pune running club was comprised primarily of people who spent time overseas and expats.
During a conversation with an auto driver, he told me that Indian's don't do "poses" (i.e., yoga) - "that stuff is just for tourists". (I gather there is some regional variation.)
So my guess that the reason India doesn't have a lot of medals is that people just don't care to compete for them.
IMHO, with a billion people, I believe that BOTH a) your generalization is true, i.e., the majority is disinterested AND b) not relevant w.r.t. Olympic medal-winning potential : it is enough for a small minority to be interested in sport / fitness & glory to make the cut for the olympics. I believe that the 80/20 rule applies, and is actually more of a 95/5 rule in most societies and most achievements : 5% of the population account for the glory (, the rest just wake the flag and feel proud, conveniently forgetting that one cannot be proud of what one did not achieve personally).
I suspect you might find a similar proportion of everday Chinese equally disinterested in "poses" (not sure, just speculation).
I believe that the core reason is our usual friend, corruption and red tape. It's not just sports; in general, the meritocratic lose out because wherever there is an opportunity in India, whatever be the form of opportunity. That includes what is rightfully yours, such as welfare handouts, your passport, etc; An Indian's everyday life consists of jumping through hoops to get basic things done.
There certainly is some 95/5 rule, or probably a 999/1 rule. But you need to apply the 999/1 rule to the people actually interested in going for the gold. I.e., in the US that might be 0.001 x 25% whereas in India it might be closer to 0.001 x 5%.
My issue with theories like corruption/red tape/etc is that India is not unique in this regard. India is pretty bad with corruption, but Jamaica is too. Yet Jamaica tends to perform pretty well - running is popular there. You can find plenty of corrupt and poor countries that outperform India, particularly if you adjust for population.
China is a special case since the government basically forces people to shoot for Olympic gold in marginal sports (e.g., discus, javelin) and trains them from early ages to do so. They also use eugenics to breed top athletes (Yao Ming is one famous result of this), and similar things.
> China is a special case since the government basically forces people to shoot for Olympic gold in marginal sports
This is a common misconception. No one is "forced" to participate in the Olympics in China. Poor parents send their children to Olympic trainers because if their children do well, they'll get to go to college for free and have a good, middle-class job.
I'd regularly go jogging. People would stop and stare - doubly so if I stopped running and did pushups. In my entire time there, I saw perhaps 3-4 Indians running, and considerably more foreigners. The Pune running club was comprised primarily of people who spent time overseas and expats.
During a conversation with an auto driver, he told me that Indian's don't do "poses" (i.e., yoga) - "that stuff is just for tourists". (I gather there is some regional variation.)
So my guess that the reason India doesn't have a lot of medals is that people just don't care to compete for them.