The calcium will leach away leaving carbolic acid behind, that re-acidifies the soil so you have to reapply the calcium carbonate to reduce the acidity of the soil.
When you read about lime, you are reading papers prepared by folks that are totally vested in "Modern Agriculture Methods" these folks are in every segment of horticulture so that even flower and vegetable farmers are listening to the same information.
What that does is get most of the growers onboard with applying lime or sulfur (depending on the base pH starting point) to adjust the soil pH.
The interesting (to me) part of this is that while it does work, it is only a temporary fix that will necessitate repurchases of the materials, meaning the seller gets to
sell you the stuff over and over and over.
When you bring up rainforest, or any forest for that matter, you are talking about undisturbed
land, growing the same plant matter year after year, most of which is
perennial.
Farmers are more about annual plants, so they are going to till and plant and fertilize and adjust every year.
CaCo3 prices vary all around the planet and countries can have variant prices too, so it would be best to locate suppliers and get quotes from them.
Redhawk