Well thought through, good work! Though I wonder if you have any insight into what (intuition?) generates the conclusion:

For the most part, the people who have had the biggest positive impact on the world haven’t had their impact by “earning to give."

Thorough out human history it's probably true, though I wonder if that is partly because 1) "earn to give" has never been practiced to any large extent (at least to my knowledge) 2) people (including myself) tend narrate great advances/discoveries in terms discoverers and persons in close proximity to the event - but not so much to the people in the background that nonetheless made it possible. I'd like to hear your thoughts!