I don't know if I agree with that, or at least not 100%.
Your so-called increase in productivity is only from a human perspective. With the exception of GMO's and hybrids, the actual productivity has changed very little. Crop rotations don't increase productivity, they decrease the rate of soil depletion. While infinitely better in terms of soil health, they also result in a greater area necessary to grow the same quantity of food, I would define that as a decrease in productivity, where I'm defining productivity as food produced per unit area. This also means a greater amount of deforestation. While some of this wood will be used as lumber, when increasing agricultural area, most is slash and burn, which means converting carbon from plant matter to greenhouse gases, ultimately, CO2.
I've yet to see how we "care for trees". Yes, the 30% of the clearcut which is replanted is managed by silvicultural types, but we haven't made any great improvements to forest health. Sure, we prevent forest fires, but all that that means is that instead of having small fires on a fairly regular basis, the debris builds up and we end up with huge blazes.
Raising animals as food crops is not an increase in global productivity. It's definitely a good thing, but 'protecting them from predators' just means hungry predators, or from a different perspective, cutting out a piece of the food chain. Viewing predators in the Disney-esque manner as some evil beast is a terribly jaundiced view of nature. For one thing, while we have a tendancy to burn our deadfalls and eat the healthy animals, the predator takes out the sick, old, and injured.
I'm not saying that we're the root of all evil or trouble. The things that you mention are ways that we can effectively manage our surroundings to minimize the impact that we have on the Earth. However, they do not consist of an improvement on nature. They are a way of supporting an imbalance that we create through overpopulation. They are good to the degree that they allow us to sustain a massive population without denuding the Earth like a massive swarm of locusts, but they aren't improving on the way things would normally be.
Tim, while I won't go to the hippy-esque extent of Mother Earth and all that, I do believe that horrible diseases like HIV are part of nature's way of culling our herd. As we're no longer threatened by any predators, disease is really the only control left. They are sadly far less selective than a predator, but I think that as our population continues to grow, nature will keep shooting out more things to try to slow/stop/reverse our growth.