For the most part we have been doing that for decades. The US has a lot more forests now that 100 years ago (the height of logging).
It is hard to know for sure, but there is reason to believe we have more trees than even 1000 years ago. We are not allowing forest fires to clean out the dead trees which allows them to build up. This is a negative, regular forest fires burn colder and leave a lot of charcoal in the soil, while the less regular forest fires burn hotter and so release that carbon back into the atmosphere.
So I didn't believe this statement (eg: more trees than 100 years ago), bc I'm the skeptical sort. You're right though. I looked at "US Forest Resource Facts..." page 8 and the numbers are higher for millions of acres across different types. https://www.fia.fs.fed.us/library/brochures/docs/2012/Forest...
It is hard to know for sure, but there is reason to believe we have more trees than even 1000 years ago. We are not allowing forest fires to clean out the dead trees which allows them to build up. This is a negative, regular forest fires burn colder and leave a lot of charcoal in the soil, while the less regular forest fires burn hotter and so release that carbon back into the atmosphere.