If the first point is neglected and plays a role, then doesn't that mean that your conclusion is unwarranted because you assume random changes to DNA..? I have no idea what Axes model is or how that relates to the study you used to determine the probability of proteins evolving.
Who knows how complicated the interplay becomes when you add natural selection and other evolutionary forces into play. It's no longer a simple random number problem. One factor can feedback back into the other... Over aeons...
Anyway..
2. https://www.differencebetween.com/difference-between-mutation-and-vs-recombination/
Why can't recombination play a role, when it seemingly plays a role in almost all standard evolutionary processes? If it can result in a novel set of genetic information, then why is it not important?
And yes, it plays a role in population dynamics. How did you rule that out? I understand that you're talking about a novel property arising, but I can imagine that happening even just through re-shuffling of the genome, forget even the novel traits for a second... because then the macroscopic properties of DNA are different and the microscopic interactions (random mutations) can differ in their feedback to the macroscopic properties.
3. "The possibility that DNA arranges, through selection, in such a way that random mutations tend to cause beneficiel changes. I.e., emergent phenomena. There's even some evidence of this happening in some species that seem to save up mutations for a "rainy day". "
I don't know what gene regulation or expression is.... Can you speak clearly. I'm talking about how DNA is arranged and how it reacts to microscopic changes.
Let me make some random shit up to demonstrate.. Imagine a strand of DNA is
AAAABCBDAAA
or
ABDAABDBEBA
If you randomly change one of the letters in that chain, imagine the first one has 500 possible macroscopic arrangements such that the change leads to a beneficial trait... The second one has 1. Clearly the first arrangement is then favored.
Imagine that selection tends towards such arrangements that mutations lead to beneficial traits at a higher chance...but you're not taking selection into account.
This is just a simple example... it becomes infinitely more complicated once you take all the other evolutionary forces and agents, and let them feedback on each other at every level.
So how did you rule out selection that creates DNA arrangements which favor beneficial mutations, when there's some evidence that this happens in nature?