Only using “phylogenetically informative” sequences in phylogenetic analyses is not the same as sorting data in such a way to bias the results towards resulting in a consistent nested hierarchy.
Phylogenetic “informativeness” is measured based on internal consistency, not consistency with other phylogenetic analyses. Nothing about choosing sequences that provide a statistically significant “signal” inherently guarantees or even biases that the trees implied by those signals should be consistent between studies covering overlapping parts of the tree of life.
We’ve discussed this a bit before, if you recall. In comments #14-25 in this thread: