However, in-person-branch-verification is a big non-starter for me. It needs to be more convenient than visiting a branch. If I have to visit a branch, I might as well open an NRE account; there's an ICICI on every street. I checked your list and I don't see any Tier 2 cities. There's nothing all over Tamil Nadu and Kerala except Chennai.
So, in the absence of a 24/7 kiosk or manned counter in every major international airport (3-4 in each state), you need to have an option for pre-verification online/FaceTime/webcam or via document upload. Otherwise, the inconvenience of a branch visit negates any usefulness.
Also, why restrict the app to work only in India? I should be able to load money and withdraw money wherever. Just disable the payment part.