There was a huge revolution in understanding taxonomy when we started actually genetically testing various organisms. Before then, we had to categorize things based on the fossil record and based on similar structures, but it turns out a lot of very similar looking things aren't actually more related to each other than they are to very dissimilar looking things.
I do think there's an argument to be made that there should be a paradigm that describe organisms that are functionally the same within an ecosystem but genetically quite different other than "convergent evolution."