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Linnean systematics can’t be outdated, but can only be improved, because it is fundamentally consistent by being orthogonal (like algebra and computer science). Unfortunately, this means that it can’t be unambiguous with regard to process, but that’s just how life is in a big city (ie, NP surprisingly does not equal P) .
This doesn’t mean that Linnean systematics will not be challenged. Class realists (like cladists and particle physicists) will never cease suggesting and claiming that classes are real, thereby contradicting Linnean systematics and instead entering inconsistency in the form of Russell’s paradox, but thus likewise never find a single consistent partitioning of objects into classes that isn’t orthogonal. Their stupid chase for classes is pathetic. How can they even enter the idea that objects have labels saying “I’m an elephant” or “I’m a crocodile”, which we can find? How can they even pose the question: what is this object really? Who says that any object is anything “really”? This their chase for “really” is actually an eternal merry-go-round in a paradox, as Bertrand Russell demonstrated in 1901. When will class realists (like cladists and particle physicists) understand this fact? When will they cease challenging science with their ancient idea that class is more fundamental than object?
The answer is thus: never. Instead, they will consistently force science into an eternal merry-go-round between their inconsistency and scientific consistency, like an eternal merry-go-round between dividing and merging, fueled by the impossibility to reach a BOTH consistent AND unambiguous description of reality. They refuse to accept ambiguity and are thus doomed to inconsistency, whereas scientists instead have unlimited possibilities to manipulate reality, but can’t equalize NP with P. They do thus promise a final solution, but can’t manipulate reality, whereas scientists do not promise a final explanation, but can manipulate reality.
A final solution is thus not possible, but manipulation of reality is, and only science can manipulate reality. Class realism is just talk without walking the walk.
At the end of the road are difficult choices of how we shall handle our possibilities to manipulate reality, not answers to what objects “really” are.