The term Indian or India too is an artificial construct 'cause someone 'coined' it like they called any term; why then must time be the barometer to measure a term's acceptability or unacceptability ?
Besides when the 'term' India was appropriated by the State of India to weave a narrative that to speak of Ancient India and the State of India to be as one or the other naturally no one would be willing to accept that just as people would be alright with accepting the term European but not German just because the civilizational discourse, narrative, literature etc. of Germanic Nations like Scandinavians, Afrikaners, Flemish, Swiss, Frisians, Austrians, Icelandic etc. essentially make them all scions of Ancient Germania.
So South Asian is not only a more neutral term but also one that is more apt in describing what we are.