We do not deal with taxonomy at all, only with testing the presence of a barcoding gap.
I am not sure that cyanobacteria can be accepted as a typical example of all prokaryotes. On the contrary, they have very special position (phylogenetic, metabolic, function in nature, ultrastructural, they grow often in multicellular and differentiated thallus) and their diversity must be evaluated respecting these specificities. It is clear that the taxonomic classification must be different in different groups of organisms.