But I've never been genuinely tempted by tens of millions of dollars before. I can't imagine it would just be "one big moment", more like slowly boiling a frog.

I think a substantial majority of people wouldn't be tempted to do world-changing bad things for direct personal gain of even billions of dollars. But the corruption is, as you note, gradual.

And the mechanism isn't direct personal gain, but gain for an institution they control: a church, a corporation, a newspaper, a university, a nonprofit. A promise of a reliable stream of income, political influence, or other goodwill for the organization is often irresistible because the person in charge doesn't feel selfish or corrupt when accepting those benefits on behalf of an altruistic mission rather than for their own personal gain, so their conscience doesn't kick in quite as sharply.