Such organic additives are much larger on the molecular level than the dissolved ions of the salts and can clog the nozzles much faster. This is actually a known problem - I am not speaking from my own experience, I only grow on coco. But as my tank looks right now with organic additives I would not give that through fine nozzles I think.Organic and organisms are not the same… how can beneficial organisms cause problems? Its done in hydro as well which you dont want organics in either.
what disadvantages? You neglected to look at the advantages that fogponics provides over the others you mentioned.
There will definitely be challenges but in the end it should provide similar growth to aeroponic which is faster than both the systems you name.
For the disadvantages of closed systems, I recommend the article on manics