Remember that the Linnean system came about before Darwin proposed his theory of common descent. Like Mendeleev's periodic table of elements, it must have been remarkable that animal species (and later plant species) could be arranged in such a heirarchical system.
Once common descent was proposed, this classification became very important evidence for this theory. The system retained its importance over the years, as new living species that were discovered, and, more importantly, the multitude of fossil species also fit very nicely into the system, providing further evidence for common descent.
But you are now correct. There is no longer any reasonable objection to the theory of common descent, and since the Linnean system is possible only because of common descent, then the logical next step is to use common descent directly in classification. I am a big fan of cladistics (even though I am not a biologist).
Still, one can see why some people would prefer the Linnean system. One really wants to say the lungfish, for example, are obviously fish, and, despite a phylogenic relationship to tetrapods, it does almost seem perverse to group lungfish with mammals as a group that is very separate from the teleosts. Stephen J. Gould even remarks on this in an essay (although I forgot which one).
There is certainly nothing wrong with grouping and classifying species according to physical and molecular morphology. All classifying systems are arbitrary. However, I feel that since the Linnean system is really based on phylogenic relationships to begin with, going directly to cladistics is a bit less arbitrary.
Edited to add: I don't see this post anywhere; I may have hit a wrong button. I am going to submit it again and hope I don't make a double posting.
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