I'm also still learning the benefits of harvesting. Do you ever harvest wheat or rice? I did in a recent game to get a city I settled mid game to jump in growth, but I was torn if it was the right decision or not.
I still am reluctant to ever harvest resources, but maybe (probably) I should be. For some reason I feel guilty destroying my stone or copper and I worry my city will need it later on, even though these resources don't provide much benefit anymore (I'm used to previous iterations where they were more valuable). I'll chop my forests and jungles though.