If you accept funding to do something to help the world, you're not helping the world unless you're underpaid, and the degree you're helping the world is proportional to the degree you're underpaid.

This is not remotely true. The implicit assumption is that life is a zero-sum game, and payment constitutes the annihilation of wealth. In reality, payment constitutes the transfer of wealth: when you spend your money, you're providing income to the people who provide you with goods and services, and enabling them to purchase goods and services from their own suppliers, etc. Economics is a positive-sum game.