Lumber is a crop.
There's no particular reason to run out of trees any more than there is to run out of corn. A farmer who harvested a crop of corn and didn't replant would be considered an idiot.
Admittedly, this wasn't true in America's early "Paul Bunyan" days, when the forests looked infinite, but sustainable-forestry wood products are a lot more prevalent now. Home Depot even makes a selling point of it.