One reason this American (me) says "South Asian" is because here "Indian" also means "indigenous North American".
If hypothetically the government of India were to declare that the name in English of the country shall in the future be "Bharat" or "Hindustan", Americans would rapidly switch to the new name, and I would no longer be tempted to say "South Asian" when I mean Indian.
If hypothetically the government of India were to declare that the name in English of the country shall in the future be "Bharat" or "Hindustan", Americans would rapidly switch to the new name, and I would no longer be tempted to say "South Asian" when I mean Indian.