The thing is, why would anyone voluntarily use a censored/restricted app store?

For Apple hell yes, maybe their government app store will be less anal than Apple is with their own app store, and e.g. allow other payment channels and allow embedding other rendering engines than Safari.

For Google though ... why wouldn't one just use the Google store instead? It's pretty open, and if their government's motive is to just create a subset of the Play store that doesn't have Chinese apps, why the hell would anyone use it?

And if the government is forcing the entire population to use its app store -- do they have the authority to do that? I thought India was a democracy with free speech.