Why is it you people always assume I'll be WORKING my forests? At size 14 with 6 forests I don't necessarily have to work any of them. Maybe one on a plains hill, but preferably none of them until RP opens up lumbermills. And then lumbermills with RRs, those forests become basically like a workshop that adds health.
Yes, "chop everything" gets you a better axe rush. Yippee skippee. Pray to the civ gods you're on Pangea for the built-in insta-win, otherwise you shot your wad by the time you can sail anywhere.
I'm not assuming you work your forests, you say you can grow your cities larger because you use the health benefit provided by forests. I don't agree.
e.g.
say happiness plays no role because of HR
You have a city with 8 health, at a stable 11 pop. you keep 6 forests, giving you 11 health total, so now you can heva a stable city at size 11, no unhealthiness and 22 food producted.
I have a city with 8 health, I chop the 6 forests, so my health is now still at 8 but I have gained hammers. But my citysize isn't stable anymore, so I will need to produce 3 more food than I did before I chopped my forests. That's one less mined plains hill I get to work, 4 hammer/turn.
So I took alot of production now, for a unknown period of lower production.
Now if I don't use that production, I will indeed be worse off in the long term. But, if you repeat that for the 8 cities people say you should have at 0 AD, you're talking about a substantial army available far earlier than if you worked all those mined plains hills.
Then I take that army, and use it to conquer land, resulting in more health, more happiness, more overall bpt, more overall production and more population, including the population in the original cities where I chopped the forests.