it staggers me that folks would spend, say, an hour clicking some dumb tab to earn the charity 10c.-timns
I think you're missing the point of the Chrome for a Cause.
As I understand, if all you do is open a billion tabs then you will probably be "disqualified" for gaming the system. The idea is that you probably open and close a lot of tabs during the day during your
normal browsing routine. So wouldn't it be great if by
just doing what you do every day your actions could contribute to a charity? With no extra effort or money on your part (aside from installing the extension and telling it which charity to donate to)?
It certainly makes what is potentially otherwise meaningless and generally a waste of time do some good for once.