This is a partial truth. While most trees used for pulp are grown on tree farms, a lot of wood used for home building and hardwoods does not come from them.
Bigger threats to trees is encroachment by urban landscapes on forests. We won’t be running out of trees, but we can run out of forests. Yes, there is a difference
The Amazon’s problems is partly from lumber demands, but also slash and burn farming. Since S&B tends to be the domain of poor natives, and the lumber industry is evil capitalism, many environmentalists have found the latter a more palatable target to attack. In fairness, a lot of the less screechy environmentalists have been working hard on solutions to replace S&B farming.
Costs for recycling next to costs for landfilling are a bit of an invalid comparison. Landfills tend to fill up, and starting new ones in the area is an urban planners nightmare. Nobody wants one near them, but you can bet people built houses not far from the old landfill. The result? Landfills must be moved further and further away from urban centers, meaning more fuel costs.