CO2 plays no role at all when burning wood. Whether you burn the wood or the tree in the forest simply dies is completely irrelevant because only the amount of CO2 can be released,
OT: No. You have turned a tree into CO2 in the stove within a few days. Leave a tree lying in the forest and check back after 15 years. It is still there. It now provides habitat for fungi and various small animals. It also provides sun/windshade near the ground against erosion.
The renewable raw material is, in my opinion, a very big fig leaf.
BTT: Here in the forum you will find a similarly polarized view on fireplaces as with vinyl vs. parquet. We let it go because, first, the money for this "gimmick" could no longer be prioritized. Secondly, we got scared that the place might simply become overheated.