Why Nested Hierarchy is NOT evidence for the ToE nor Common Descent

The main reason why nested hierarchy is not evidence for the theory of evolution nor Common Descent is that neither would be phased if it wasn't observed. That is obvious because nested hierarchy is not observed throughout the diversity of living organisms on this planet.

Denton page 129:

Cladism takes no account at all of any evolutionary claim regarding the genealogy or derivation of any particular species or group. Cladists aim only to discover the pattern of nature as it actually is.

page 131:

"Yet, direct evidence for evolution only resides in the existence of unambiguous sequential arrangements, and these are never present in ordered hierarchic schemes."

IOW If life descended (along uncrossed lines) from a common ancestor, it would form an unambiguous sequential arrangement, which are never present in ordered hierarchic schemes.

But that point is moot because we know that lines can be crossed, that is that traits can be gained and lost only to reappear later.

In fact, a nested hierarchy is the almost inevitable result of descent with modification, if no transfer of traits between branches of descent is possible.

With the ToE and Common Descent a transfer of traits is possible between branches. I will also note that any such nested hierarchy referred by EvoWiki would not conform to the rules of hierarchy.

And seeing that Nested Hierarchy was and still is used as evidence for a Common Design since before Charles Darwin, one would think that evolutionitwits would get their own evidence as opposed from just co-opting their opposition's evidence and scheme and re-labeling it.

ADDED VIA EDIT:

And finally the only way that nested hierarchy could be used as evidence for either the ToE or Common Descent is if and only if, it was observed in the diversity of living organisms and there alone. However we know that is not true.

Zachriel provided the following:

The nested hierarchy is a pattern. Like all patterns, it can be defined mathematically and exists outside of biology. A nested hierarchy is an ordered set such that each subset is strictly contained within its superset.

Now I am sure that bit will be lost on Alan, Zachriel and their ilk. But that is to be expected. It is a prediction that follows from their condition. And what may that condition be?

See for yourself