No need. I have 3 citizenships from other developed countries but they look at place of birth, citizenship of parents and even grandparents. Last time, I applied, they even checked on the citizenship of my wife as well as any other citizenship held by her. I had to provide even passport details for my parents. So, your suggestion would make it a little better but it remains difficult. Now they have a visa on arrival as well as eVisa but it’s not allowed for foreign citizens of Indian origin, unfortunately. India has the same policy towards them and they sort of reciprocate.