Rotten bogs may turn into a natural fertilizer in very few days of time.
No they don't, and they are about the only terrestrial environment which does not. They turn into coal beds and sequester carbon under the surface of the earth for millions of years.
https://www.dkfindout.com/us/animals-and-nature/habitats-and-ecosystems/rotting-log/
Which will turn into a place for million tiny organisms and also stops soil erosion.
Forests don't form coal beds. You should be able to verify this by simply going for a walk. Peat bogs and swamps do. The bio-accumulation overloads the ability of insects, fungi, and microbes to break down the hydrocarbons and turn them back into CO2.
Living roots are the primary method by which erosion is hampered. Cutting down a forest can cause big problems with erosion in some environments. Of course in other environments large tree roots force apart rocks so it's a mixed bag.
But generally one of the only real problems with timber harvest (and forest fires) has to do with silting of streams and in some cases landslides for a relatively brief period following the harvest. Another problem is increased solar radiation on streams which can increase the water temperature. In places where there is responsible harvest practices a buffer zone is left.
In places where the 'watermelons' have gained power these 'buffer zones' are expanded to ridiculous levels. That's a social issue related to some people's political feelings about ownership of private property. Has nothing to do with science or protection of the environment (even if the 'useful idiots' think it does.)