If that were true, then you’re saying Linnaeus has the same problems as before it, and it only split people up? Maybe we should go back to the previous names? Of course the system could be improved and solve some problems, the relevant questions aren’t whether it’s possible, they’re about goals, scale, and agreement.
Feynman’s quote is cute but doesn’t seem completely relevant to a hierarchical taxonomic naming system that in fact does tell you something about what a bird is from the name, no?