The problem here is that you are not allowed "incentives to click artificially on sponsored links". And the implied message of "click a link, plant a tree" is clearly and artificial incentive, even though there is a disclaimer no one reads. It makes these clicks less valuable (lower conversion rates), advertisers still pay full price, are unhappy, and because advertisers are the true Google customers they make sure it doesn't happen.

But the question would be: why not make "charity clicks", which advertisers can opt in or out of. The best, if a little evil part: good PR for everyone involved. The "plant a tree" search engine gets to grab people. Advertisers can say they support charity by allowing such lower value clicks to go through and Google can do the same. i.e. for one good action, 3 parties can claim responsibility.