The immediate gain from chopping followed by the health and global warming problems, or forgo the chopping for fewer future problems.
I agree, as above, that that's how it's meant to work. But sadly I don't think that's how it does work. The health problems don't really count because you've only got to generate 2/5 of a food per chopped forest to get back where you started. The global warming problems don't encourage forest preservation for three reasons.
Firstly, you've got to survive to the point where it's an issue; you can only afford to take long-term benefits over short-term gain once your empire is well established, and when you consider chopping out your first settler, you are anything but well established.
Secondly, as in reality, the nation that chops or pollutes gets the benefits, but the disbenefits are shared evenly - and worse yet, you're much more concerned with relative empire strengths than absolute prosperity than you might be in reality. Let the whole world be desert, provided I own half the desert; I'll still win the game. To make the mechanic work in Civ you'd have to have diplomacy benefits for taking action, or extra benefits under Environmentalism [1], or something.
Thirdly, it's academic because the AI will chop all the forests it can anyway, and global warming is inevitable.
I think the description of it as an afterthought is fair enough. I see how it's all meant to work, much like you describe. But it doesn't, because the answer is, 99% of the time, chop away and chop the lot.
[1] Incidentally, I'm often struck by the irony of thinking "Environmentalism? Great. Now we can build lots more factories and coal-fired power plants."
might be helpful. IMO.
