Cute, clever, incorrect.
The Food and Agriculture Organization (FAO) of the United Nations's Forest Resource Assessment for 2005 used the word "alarming" 20 times to describe the trend lines for deforestation. And, a commonplace inference is that forests are rapidly disappearing due to logging.

Deforestation, that is the conversion from forest to non-forest, is not necessarily due to logging (illegal or otherwise). So it is not greed, but survival that often drives deforestation. About half of the wood consumed in the world is for heating or cooking [Global Forest Resource Assessment 2010 - Key Findings] with much greater rates of consumption for fuelwood consumption in Africa and Asia.

The primary culprit is conversion to agriculture, often by poor farmers, followed by wood for heating and cooking. Fires, slash and burn agriculture, mining, and hydro-electric projects also cause deforestation.

A 1996 report by the Consultative Group on International Research (CGIAR) report states that deforestation is often done by people trying to eke livings from the land:
[T]he main threat to tropical forests comes from poor farmers who have no other option to feeding their families other than slashing and burning a patch of forest and growing food crops until the soil is exhausted after a few harvests, which then forces them to move on to a new patch of forest land. Slash-and-burn agriculture results in the loss or degradation of some 25 million acres of land per year (10 million hectares). "Some 350 million people in tropical countries are forest dwellers who derive half or more of their income from the forest. Forests provide directly 10 percent of the employment in developing countries," says Jeffrey Sayer, Director General of the Center for International Forestry Research (CIFOR), based in Bogor, Indonesia, which researches better ways to manage and preserve existing forests. CIFOR is one of two CGIAR research institutes that specialize in tropical forestry.
Once the primary causes of deforestation are obvious, it becomes equally obvious that lowering the demand for wood (by using less wood or substitutes) will not make a difference in lessening world deforestation. It's not the demand for lumber or paper that drives the cutting. It's the demand for farm or pasture land, or the demand for heat from burning. What's the answer?

Poverty drives much of the demand for firewood and land for farming; the poor have few options. The lessening of poverty may be the greatest steps we can take to halting deforestation.