Biometrics alone aren't sufficient, but they're a reliable way to prevent identity theft
if you have a secure record linking the identity to the biometrics - there will be people with similar faces and may be fingerprint matches, but fraudsters aren't going to easily find a thief that happens to look similar to you, match your fingerprints, and forge a document just to get a small loan or some electronics on your credit. The point is that biometrics can't be treated as "something you know", and the system should be designed in a way that these biometrics getting compromised isn't a big problem; I mean, my EU ID card has a chip with my fingerprints on it, but getting a copy of my fingerprints won't really risk "my identity", all they're good for is to prevent someone else using my documents if they steal it even if their face looks similar.
Getting such a secure record, though, generally requires a decent level of gov't infrastructure throughout all areas, and can't be built up quickly. Size alone isn't an issue - if it works for half a billion people in EU, then it'd work for a billion people elsewhere, but the infrastructure needs to be there.
I.e., you need a population where all or nearly all births have been properly tracked and reliably registered for a long time, so you can't build it faster than decades if it wasn't the case; you need a general low corruption environment where mass issuing of fake IDs by corrupt officials won't happen (a limited number of fakes by organized crime might be inevitable, but they won't disrupt the system); you need an effective policing system where everyone, including the most poor, would report stolen wallets and documents to be revoked; you need effective infrastructure where it's trivial for everyone giving credit or goods "on lease" to verify online the validity of some documents.
I'm not sure how it's in India, and I assume that some of these might be a problem, but for USA (as the original article) all these things are in place and such an ID would work if it was implemented.