I definitely understand that the majority of taxonomies are problematic for the reasons you cited. When OP said "no such thing as a tree", I thought OP meant a taxonomic tree, not a literal plant tree, hence my example of binary numbers! Thanks for clarifying.
That said, taxonomic groupings can have both wide consensus and be useful, can't they? (Hand on chin... monotremes? hominids??)
The CS specific analogy might be, "Abstractions are leaky," or more broadly the, "map is not the territory."
Any complex-phenomena that is modeled with with a simplification will have places where that simplification fails. But models can still be highly useful, you just need to choose an appropriate level of abstraction, accept and manage any tradeoffs with exceptions, and move to better paradigm if one emerges.
Although if you want to get get technical, even evolutionary relationships are only trees if you throw out some of the information that doesn't fit the tree. It's truer to speak of phylogenetic networks that can take into account things such as horizontal transfer of genes and recombination.
That said, taxonomic groupings can have both wide consensus and be useful, can't they? (Hand on chin... monotremes? hominids??)