Wow I was surprised by this figure, so I tried to find the source everyone quotes. It appears to be a 2006 telephone survey of 987 randomly-selected voting age citizens that were then weighted for an underrepresentation of race (so perhaps not that accurate). Anecdotally, I work in a safety net hospital and it is really rare for someone to come in without ID, which is why those numbers seemed so surprising to me...
Pretending that government IDs are super duper hard to give out is a time-honored American tradition.
After all, imagine if the government had a database with every person's name in it! You'd have like 300 million rows? Nobody's built a computing machine that could do that. And then how would you get the cards to people? You'd have to send out horses and buggies to every corner of the nation. And where would you find enough coachmen to do that, and roads to drive the coaches on???
No, clearly it's unpossible.
So we have to reserve the use of government IDs for really important things, like checking if you can buy cold medicine, and voting must remain insecure.
Government IDs are not a solved problem, and you don't seem to have even tried to consider the issues involved. The key distinction between voting and cold medicine is that you have a right to vote, but not to buy cold medicine. So if you lost your ID, or it's expired, it is not an option to just say "that sucks, I guess you can't vote now".
In fact, as a rule, ID is reserved for things that aren't important, because it is a point of failure.
The point of India requiring identification for benefits is to prevent waste and fraud. And given the number of poor people in India, and the limited amount of money they have to help them, it seems like quite a good thing to do so.
Identifying people is not hard, even for the poorest countries, and it's quite easy to do with modern technology. There is no good-faith reason to oppose it, any more than there is to oppose driver's licenses.
https://www.brennancenter.org/media/6697/download
I could easily have missed a better or more recent study, so if anyone has one please post it!