It can be a large economy, in part because there are 1.3bn inhabitants, but my point is that people consume services provided by Indian companies largely because they are cheap.
This does not seem true. Indian service sector is very good at its job barring a few bad apples. For example, FinTech industry has done a remarkable job of easing payments. Compare that to Germany where the service sector is just awful. Of course, German competency in manufacturing is far ahead of India right now. It would be great to see both countries fixing up their weak areas in the future.
That may be true but Indian fintech is for domestic use and we are talking about exported services.