If a whole forest grows and the whole forest dies, you’re right, no carbon is captured.
But if a whole forest is created and maintained, even as trees die and rot they build the biomass of the soil and undergrowth: every ton of life is carbon and heat energy captured - individuals live and die, but the overall biomass can increase, capturing carbon and energy in the form of healthy ecosystems.
As another commenter pointed out, if humanity just left earth tomorrow, it would take eons for CO2 ppm to fall, so we should be doing something proactive. Plus, planting and caring for trees is something everyone can do and gets us away from the “wait for a super villain billionaire to solve it” mentality.
Edit: thanks for the link to Azolla, hadn’t heard of that
We would need to recreate the Azolla Event: https://en.wikipedia.org/wiki/Azolla_event
Or even the Carboniferous period where microbes could not digest lignin and cellulose: https://en.wikipedia.org/wiki/Carboniferous
Which is impossible. We simply need to stop digging fossil fuels out of the ground in order to burn them.