>>I would say the point is that paraphyletic taxa preserve mistakes and traditions.>>

Paraphyletic taxa are not "mistakes." Polyphyletic taxa are mistakes. When uncovered, polyphyletic taxa are removed from the classification. For example, Pachydermata, a polylphyletic taxon consisting of elephants, hippos and rhinos, is no longer recognized even though it is an old taxon. Paraphyletic taxa are actually the inevitable result of the process of evolution. If you don't understand it, that is okay. I will explain.

Turn the clock back to an early stage in the history of life, when there is only a single genus and a few related species, all of them not very different from one another. Move forward a couple of million years, and we see a new species which is different from all the other species existing at the time. A taxonomist is now faced with the decision of whether to continue recognizing only a single genus or place the new distinct species in a second genus. Recognizing a second genus automatically causes the old genus to become paraphyletic. Is the erection of a new genus "subjective?" Yes, certainly. Is it bad? If you are a cladist, you would probably think it is a bad decision because you don't like paraphyletic taxa.

So, what should be done? One genus or two genera? Of course, whether taxonomists call these groups of species one genus or two genera has no effect on the welfare of these species. The only reason why we even bother to consider the question of one genus or two genera is because of convenience. It is far more convenient to refer to all the species found in one genus using the name of the genus, instead of having to refer to all of the species by name. Hence, the reason we classify is that it helps us communicate with each other. So, what does the dogmatic belief that paraphyletic taxa are not acceptable has to do whether a classification is useful or not? Yes it does. That is because if we do not recognize paraphyletic taxa, then we cannot recognize a second genus at all. All life on each therefore cannot be classified in more than one all encompassing genus without violating the no paraphyletic taxa rule.

>> Paraphyletic taxa only make sense if people wish to base phylogeny on subjective perceptions.>>

Certainly. One must rely on subjectivity when judging amounts of differences between any 2 species. But how else can we decide whether and how to classify organisms unless we rely on judgment? Should we flip a coin or play a game of musical chairs to decide whether one species should be classified in one genus or another? How is coin flipping going to result in a better classification? Flipping coins is very objective, because there is a 50-50 chance of tail or head. So, you worship objectivity. Unfortunately, objectivity is not a cure all.

>>For example: many can accept a taxon made up of species with bony shells, hollow venomous fangs, rattles, hemipenes, and heat-sensing facial pits... but not fur or feathers.>>

As I said, taxonomy is a democracy. If you think it is stupid to recognize a taxon that shares the synapomorphy of fur or a taxon sharing the synapomorphy of feathers, then you can certainly publish a taxonomic proposal to disqualify these taxa. BTW, hollow fangs have evolved independently in the elapids and the crotalids. So, it is a convergent character that cannot be used to define a taxon. Thought you may want to exclude hollow fangs from your argument the next time you make it. Also, fangs are not themselves venomous, but they are used to inject secretions from the venom gland that is located next to the teeth.

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