What is the advantage of using plant-derived antibacterials rather than bacteria-derived antibacterials?
Bacterial isolates from ancient permafrost and isolated caves allow study of the resistome, or the collection of antibacterial resistance genes, in environments without exposure to modern antibiotics for medical and agricultural use. These samples have genes for resistance to antibiotics derived from a variety of sources, including fungal sources (penicillins, cephalosporins) and synthetic dyes (sulfonamides), as well as bacterial sources (macrolides, aminoglycosides, etc). This finding was surprising, but does help explain the rapid emergence of resistance in response to clinical use. The genes have been there all along.

The OP is correct that a great deal of our current armament of antibiotics were derived from bacterial products, but since fungal and wholly synthetic products don't solve the resistance problem, I don't believe plant products will either.