I see this as not great from an environment point of view: the anaerobes in the unturned manure will go, well, anaerobic and generate a lot of methane.
I wonder how much methane you could capture from a domestic-sized greenhouse, fertalised with manure? I'm really not sure what paths there are for manure which don't release methane and other emissions, at least here the effect is useful
> what paths there are for manure which don't release methane
Aerobic digestion. Ie: with lots of airflow/oxygen (lots of heat also helps!)
That will happen whether you do this or not.
Not in aerobic digestion. Then you get much less greenhouse-gassy CO2 (with the side benefit of being great for immediately nearby plants).