Why the insistence on pure randomness?
Mutations are not randomly distributed throughout the genome, the chemistry of the DNA string makes some areas more prone to mutations than others. Some areas of the genome are more prone to ALUs. Some areas are corrected more faithfully than others.
Selection isn't random either. Once the mutations have increased the range of allele variation, the numerous modes of selection, working singly or in tandem, determine the direction the population will take.
You can't define 'random' to mean 'everything not directed by an intelligence'. There are many natural phenomena that produce nonrandom results.
Randomness or external bias is the essence of the debate between Evolution versus Intelligent Design.
Randomness can occur without any form of intelligent intervention, after all.
So do we have a DNA-processing-engine and a DNA data-structure with designed redundacy and some level of error detection/correction...or do we have purely random chemical interactions?