What if genomes of organisms didn't appear related?

In my opinion, one of the more compelling lines of evidence for evolution is that we can sequence the genomes of any living organism nowadays, and what we've found is a striking similarity among organisms. For example, and oft-quoted number is that the genomes of humans and chimpanzees are 99% similar. Pretty good evidence for common descent, is it not?

And by the way, this isn't exactly a new thing; it isn't just with the dawning of the post-genomic era that this line of evidence was put forth. There was a seminal study by I-forget-who back in I-forget-which-year where a graduate student was determining the primary sequence of some proteins in different organisms. She was attempting to show that these proteins were different in different organisms, and was dismayed to find that there was striking similarity. Her advisor being very wise (as advisors usually are), quickly saw the high-impact factor of such a find: this was concrete evidence for common descent!

Anyway, back to my main point. Is this similarity in genes and proteins and whole genomes compelling evidence for common descent? Or is there a way to explain it from a "God-created-it" standpoint? After all, if you're a creationist, you may not have to explain the mechanism by which genomes became related, but you do have to explain why God would do it that way.

One of the counter arguments is that God used a common design template when creating organisms, and only modified this template in small ways to account for the different purposes that He had for the different organisms. After all, there's no need to reinvent the wheel. In essence, this is arguing that God designs life in the same way that engineers design machines they build.

This argument doesn't really sit well with me. It's not that I don't think God would design life in the same way engineers design machines. To the contrary, I am convinced that He would, or perhaps more appropriately, we design machines in the same manner that God designs life. No, I am uncomfortable with this argument mostly because it's too hand waving. It doesn't have any real substance to it.

I prefer to put forth a counter argument from the basis of the question: What if God had done it another way? That is, what if genomes of organisms didn't appear related?