Carbonic acid is unstable, and quickly decomposes back to CO2 and H2O; to later recombine. Between the constant creation and decomposition of carbonic acid, very little of the CO2 dissolved in water actually exists as carbonic acid at any moment in time.
So unlike other acids (sulfuric, nitric, etc.), concentrated carbonic acid cannot exist. Even if you could somehow instantaneously summon it into existence, it would decompose so rapidly into CO2 and water that it would turn its container into a bomb!
If I recall correctly, the maximum carbonic acid concentration is a mere three times the amount in a can of soda. There have been some successful experiments supplying carbon to plants by regularly pouring in sparkling water; but the amount and expense required makes this a novelty rather than a useful method.
Sorry. It was a good idea though.
(EDIT: Just read that you "have your sources". Since carbonic acid at a useful concentration is impossible, you may have seen carbolic acid
instead. Don't confuse the two. Carbolic acid is a highly corrosive disinfectant, not a source of carbon.)