Nested hierarchies are an artifact of design. Human designers create nested hierarchies constantly without even thinking about it.
No, human designers do not create nested hierarchies (of any significant numbers of items) because they are free to "cross-pollinate" characteristics from one item to an unrelated item.
A nested hierarchy such as life's has
absolutely no duplication of labels. All labels are unique.
I challenge you to produce a nested hierarchy of, say two dozen man-made objects of your choice with at least four levels that does not duplicate labels or cannot be easily shown to require duplicate labels to be extended.
Many have tried.
All have failed.
Here's an example. It does not duplicate labels, but it does require duplicating labels to extend it significantly. Can you see why?
Your argument is only convincing if you assume the "random-creature-generator" absent of evolution, whereby you then invoke the "infinite possibilities" aspect, no one more likely then the other.
Nobody has claimed a random uniformly distributed "creature generator". But we have observed a fact; there are many possibilities of how life could be organized that are not a single nested hierarchy. That fact screams for explanation. Got one? Why do we see what we see?