While it is of minimal import what you in particular would expect, still, I wonder why you would not. If a parent - be it an individual, or a population - has several offspring, all of whom are similar but not identical to the parent, then those offspring will share a majority of characteristics by which we can classify them as related: the similarities you are happy to acknowledge. If now those children each or mostly have children of their own, those grand children now share with their parents about as much as the parents did with one another, and as they do also among each other. However, cousins will share less in common than siblings, or parent-child pairs, and parent-grandchild pairs will also share less in common than siblings or parent-child pairs. They will still be highly similar, but the differences will stack up, since it is unlikely that the changes between one parent and its child will be reversed between said child and the grand child. As generations pass, each generation will be typically less similar to the common ancestor, but most similar to its immediate siblings and first cousins, than to any more distant cousin.
That is the expectation we have from the basic assumption that reproduction yields descent with minimal modification: We expect, that if organisms share ancestry, that the differences in their genes will have these structures, where some change happens early, gets inherited, and sometime down the line new changes happen, usually in other loci, and, too, get inherited. We do not need to assume common ancestry, or particular familial relations at all, but when we see genetic markers form exactly this sort of pattern where one can classify which variants are modified versions of which other ones in a single direction, this is perfectly consistent with common ancestry, not least of which because genes are the literal substance of inheritance by definition.
Common design, on the other hand, has no reason to yield any patterns of such kind at all. It is free to make changes that are in no way at all based on the immediate parent, but can go back and reverse all arbitrarily old changes for any reason, or introduce de novo designs completely foreign to the entire family at will. Common design, while not impossible given the data - as no data could hope to falsify common design; a weakness of that model, I should opine - is in no way positively indicated by it. We would not expect the data to be as it is assuming the model, since the model does not entail the data being as it is. Our experience with design patterns, if anything, would lead us to suspect otherwise. We could of course also speculate that part of the designer’s intent is to deceive us into thinking descent was a better account of his design, by making said design look exactly what we would expect to look like and nothing like what any known design looks like. Personally, I find this excuse rather reaching. If that is how far we are willing to go to defend the idea of design, then there is no reason that can reach us on this subject.