Here is a straightforward reason that no one who claims to be some sort of economist (social or otherwise) can argue against:
India has 1.2 billion people and is not particularly endowed with wealth that it can dig out of the ground. So the only way to create wealth is to turn 'sand-into-silicon' aka make productivity gains using the only abundant resource it has - the human resource.
Now if this particular mission can inspire .0001% of additional population to aspire for non-manual labor employment (i.e. study STEM etc), the productivity gain from those people will pay for this mission many times over (I haven't cared to do the math here because I just want to illustrate what I thought is an obvious point which people somehow gloss over).
Population of India: 1.252 billion people.
0.0001% o that: 1252 people.
GDP of India: 1.877 trillion USD.
Per capita: 1499.
So if we just applied these figures to the above number of people, we get an increase in GDP of 1.876 million USD. Which is not much. I know you were making a point.
I think this is an unfair calculation because it's not taking into account the fact that those people will go into STEM-type jobs. So it might be a good idea to compare it to the IT industry of India that produces revenues of 100 billion USD using 2.8 million people. That's 35 USD per person.
Combining this figure and the one above yields a rough GDP increase of 45 million dollars. We're certainly getting there in terms of order of magnitude.
To put things into perspective, 0.0001% is 1 in a million!
