It was. The question is, was it done to create arable land, or to boost production?
To the best of my knowledge, ship building was the primary impetus to cutting forests for production. Other uses for wood (buildings, etc.) didn't particular de nude the landscape, but periods of heavy investing in ships did, both in the ancient era around the Mediterranean and then again during the Age of Sail.
I think you're underestimating the capacity for growing cities, and civilizations, to impact the surrounding landscape - sometimes smaller communities could be particularly bad at ensuring forest sustainability. In the middle ages extensive deforestation took place in parts of Europe, including Great Britain, primarily
for fuel. Firewood to get a single household through a cold winter is substantial; a small village could easily keep cutting 'rings' around it each year until the forests became to distant to easily extract timber from.
Fire was critical to every aspect of life and would be maintained non-stop. Now, this was indirectly productive as it enabled people to do things and produce things that they otherwise couldn't.
It was also used for building everything from furniture to homes themselves. This includes most buildings - often all - in the urban areas. Imagine the amount of timber required to build the cities of Europe (over and over again). Now expand that across the world.
Early European states were engaging in large-scale forestry management as early as the 17th century, following the Peace of Westphalia that brought the 30 Years' War (and a few others) to an end - and, almost accidentally, established the first widely held concept of
sovereignty. Ship-building was important to many states, but construction within cities demanded enormous production well before the industrial revolution.
Many early modern states, and some larger pre-modern forms of governance, actively engaged in protection of forests for economic purposes. Forest protection was practiced, approaches were developed to ensure that entire areas weren't deforested, etc. all long before industrialization.
In parts of Southeast Asia, where my expertise lies, swidden agriculture would lead to some deforestation during periods of high internecine warfare, when the population of the mountains were beyond the reach of the mandala states such as Pagan to Sukhothai. However, the deforested areas would be used to build villages from the forest material - but the nature of swidden agriculture leads to semi-nomadism. Though in the industrial era, in Siam the Royal Forestry Department had been established as one of the most powerful institutions of the state by 1900 and remains one of the most powerful arms of the Thai state to this day - this is a direct result of the region's history of forest management.
TMI???
(Edit: fixed grammar, added some info - sorry, heavily medicated right now!)