> It is simple enough to be reachable by a dumb, brute-force, random-walking, incremental process of evolution;
I'm not an expert in this field, but from what I heard brute-force natural selection is the naive explanation we're given in school. There are many more factors at play other than random chance: e.g. there is also sexsual selection. Sexual selection selects some characteristic that isn't necessarily an advantage in the current environment, but it is somehow preferred by the opposed sex. According to some research, the reason why we lost the bone that other primates have in their penis is due to sexual selection.
One intuition that helps is to see evolution as a random search through solution space. Another thing to realize is that -in evolutionary algorithms- the distribution of random trials will be strongly biased around existing solutions.
It helps to understand that in some situations, a search algorithm with some level of randomness can arrive at a solution faster than a systematic/random approach, on average. In other situations, a search with added randomization might be slower, but its ability to escape local optimae (to some degree) means that it is much more likely to find the global optimum (or at least a better local optimum :-P ).
Interesting points. But I would add that sexual selection can select for some trait that is actually counterproductive, a famous example being peacock tails. Female peacocks use them to evaluate the health of potential partners, so it is an indirect measure of fitness to the environment. But at the same time, it is clear that healthy peacocks would still be better off without carrying around such big tails. If tails weren't so important for reproduction, they would have likely shrunk by now. I wonder how a comparison with the methods you mentioned would capture this.
I'm not an expert in this field, but from what I heard brute-force natural selection is the naive explanation we're given in school. There are many more factors at play other than random chance: e.g. there is also sexsual selection. Sexual selection selects some characteristic that isn't necessarily an advantage in the current environment, but it is somehow preferred by the opposed sex. According to some research, the reason why we lost the bone that other primates have in their penis is due to sexual selection.