You can’t explain the pattern with a “common design” strategy, because there is no mechanism on “common design” that inadvertently constrains the different gene sequences to yield consilience of independent phylogenies unless the designer is being intentionally deceptive.
You would have to posit that the designer is deliberately doing this forcing on the data for no apparent reason, essentially producing the exact pattern you would expect from common descent simply to make “common design” compatible with that same evidence. Which would make the designer act in an intentionally deceptive manner for no functional reason.
If the designer is creating genes for specific functional purposes, there is just no reason to expect those gene-sequences to be constrained in their sequence by how they should end up grouping if some decides to use them as input in a phylogenetic algorithm.
If you want a more in-depth explanation for why this “common design” rationalization of yours doesn’t make sense and doesn’t explain consilience of independent phylogenies, read this post:
This is that famous word-salad of yours again. A criticism of an explanation is not itself an explanation for anything. It’s not supposed to be. But explanations for WHY common design does not explain consilience of independent phylogenies have in fact been provided many, many times before.
It’s because “common design” is a vacuous idea that doesn’t predict any particular pattern. There is no mechanism in “common design” that produces nesting hierarchies.