I use 'arbitrary' in the sense of uniformly random. The point is it's not uniformly random. You can think of reproduction as a random walk in the space of DNA

I use 'arbitrary' in the sense of uniformly random. The point is it's not uniformly random. You can think of reproduction as a random walk in the space of DNA combinations, but it's not a uniform random walk. It has a structure that comes from the biochemical processes which perform the recombinations of DNA. Focusing on mutations ignores this point. (Also, as an aside, it's not settled that mutations occur at random positions. That may be a reasonable starting point, but it's likely that the way DNA folds into nucleosomes/chromatine/chromosomes biases the location of mutations.)