The jury is not "out" and this is trivially demonstrable. ALL programs of finite length can be produced in a finite amount of time by stupid automata. It is middling mathematics, and bloody obvious if you think about it. Your distinction between "useful" programs and all others is meaningless, nevermind that you are clearly demonstrating sample selection bias (i.e. your opinion of "useful" is not objective or random).
Engineering in a number of fields is done today by sifting random garbage on a computer; the process works and produces useful designs even though no one actually "designed" anything. Designs arrived at in this fashion are properly characterized as chance accidents; the only thing the engineers do is select interesting things that emerge from the chaos storm. Hard drives are designed this way, yet I don't see you marvelling at the beauty of the engineering even though it literally emerged by accident from random processes. If we can design high-tech equipment by letting random processes run wild, why is there a need to suggest that DNA is any different?
"The jury is not "out" and this is trivially demonstrable. ALL programs of finite length can be produced in a finite amount of time by stupid automata."
"Automata" are intelligently designed programs, not self-formed naturally. Sure, an intelligent designer can build a computer program to write other programs via various methodologies, but that's not "natural" and unaided, rather - that's directed.