But again you're artificially restricting the possible outcomes. If we consider the chances of producing anything cogent - a limerick, a haiku, a sonnet, a knock-knock joke, a single grammatical sentence - then the odds are better than just producing a limerick. And who's to say which of those is more useful?
Moreover, "useful" has to be defined in terms of what might be useful to the current state of the life form's DNA, so the oddsa re even smaller.
No, I think you're still shortchanging the situation. I can, with a little bit of thought, come up with dozens and dozens of ways to improve the human body, for example - it's not a perfect machine. And there are surely hundreds or thousands more that I just can't imagine. The fact that there are so many possible improvements ups the odds significantly. For example, here's a really short list, right off the top of my head:
Imagine that your optic nerve was placed slightly differently, so that you didn't have the blind spot that you do now. Imagine that the tendons and ligaments of your knees were slightly rearranged, such that a sharp blow to the outside of your knee was much less likely to cripple you. Imagine a slight modification to your cellular membranes that rendered you immune to a particular virus. Imagine a small change in the density of the cilia of your inner ear, such that you were able to hear sounds across a greater range, and of a higher pitch than you are now able to. Imagine one small new protein that confers a greater resistance to certain types of cancers. Imagine a slightly more efficient digestive process, such that you could survive with a caloric intake 10% lower than you can now. Imagine a slight change in the chemistry of the junctions of nerve cells such that the nerve conduction velocity was increased, and hence your reflexes were faster than before.
And on, and on, and on....give me some time, and I'll come up with lots and lots more. And there will be potential improvements that simply exceed my ability to imagine them, either because they are improvements that exist in other organisms, but that I am not familiar with, or because they'd be completely new and unique. There's really more than just limericks possible, I think. ;)
As for what the existence of DNA has proved--I would say DNA only shows the common descent, not why life forms changed. Natural selection explains small incremental changes, but not macro-changes. Some OTHER force explains macro-changes.
Actually, I agree with your first sentence there. DNA shows common lineages, and gives us a picture of a family tree. But as for why life forms change over time, for that you have to look at the environments in which they lived and died.
As for the second part, what is a large change but the accumulation of many small changes? Remember the steps in the development of the human brain? If you take only the "beginning" and "end" brains - Australopithecus and us - then the change looks like a huge quantum leap. But when you see all the intermediate steps, it becomes a rather orderly progression, and the end product no longer looks like something that just sprang forth, sui generis. It wasn't an accident that I picked that example ;)
That's an interesting intuition. Are you familiar with frame shift mutations? That's when a single base is inserted or removed in a gene. Since it's triplets of bases (codons) that determine the amino acids in proteins, if you leave one out or add one in, the resulting protein has a completely different amino acid sequence from the original.
Based on your intuition, how would you rate the likelihood that in the few years we've been analyzing them, we'd come across a case where a frame shift in a middling sized gene resulted in a new, biologically useful function? Would say it's somewhat likely or so unlikely it's virtually impossible?