Oh, but they do. Human activity was depleting many of these resources, and quite severely, even in ancient times. Besides archeological evidence, contemporary sources even mention the environmental damage. Just one example of this would be the rise of Macedon through its trade in timber with Athens in particular. By the time of Alexander, much of Attica was deforested, with the accompanying erosion, drying of springs, and declining agricultural production. The building of the first Athenian fleets and charcoal production to keep the mines of Laurion in operation had wrecked Attica. When you combine deforestation with a climate that only receives rainfall during a small period of the year, you don't get regeneration, you get desertification. Even today the Greek government struggles to plant forests in many areas of Greece.
Macedon, on the other hand, had access to larger forests and much of that territory was higher in elevation and received more rainfall. They happily traded timber to the more established, dominant Greek states while consolidating their control over that region of Greece. Of course, one can't lay the rise of Macedon entirely at the feet of environmental damage by other Greek states, but it played quite a large role. There are a few books on the subject, for example Environmental Problems of the Greeks and Romans: Ecology in the Ancient Mediterranean by J. Donald Hughes is a good place to start if you are interested (for the record, I studied classical Greece at the university).
If one wants realism in the economy of the game, then each biome would need to behave by different rules. I think this would be needlessly complicated and confusing for people to remember. Also, the game doesn't have any passage of time. We already have to suspend belief that you can plant a farm and start harvesting in minutes... I think that planting trees is a neat idea, but growing usable timber in the context of a game that lasts about 30-45 minutes is something else.
Don't get me wrong, many of these ideas are great, but are more suited to a mod. The game would be totally different than it is today. Personally, I'd love an Anno 1602 meets 0AD, but I don't see it happening officially.
Edit: For what its worth, some of these ideas could be implemented in some fashion and could help diversify gameplay or enjoyment, like animated buildings or Lion's suggestion to have "cash crop" plantations to generate coin.