I haven't yet seen a good explanation as to why this focus on randomness is so prevalent, but chance really is almost irrelevant when it comes to evolution.
The main mechanisms of reproduction and selection that you point out have almost no randomness at a population level.
Selection of individuals has some randomness associated with it, as death can come unexpectedly to anyone, but at population levels it is the genes that make it more likely for an individual to survive/pass on their genes that are the ones that get passed on. It's possible that an entire population gets wiped out, or a particular gene gets wiped out due to chance, but as long as the population is reproducing then on average the genes that are passed on are the ones that help the population survive.
Similarly reproduction isn't random at population levels either. Sexually reproducing populations mix their surviving genes evenly within geographical locations over evolutionary timescales (such as trees), or selectively if individuals choose their mates (like humans!). Neither of those things are random. Mutations that happen during reproduction are somewhat random but, as for asexual populations, the amount of mutation at the population level is not random. It's reasonable to expect the reproductive mechanisms to be selected for in such a way to maintain coding errors and the like (at an appropriate level) so that mutations continue to develop and strengthen the gene pool.
While there are lots of single events where randomness and chance come into play, as soon as you have a collection of things that reproduce those things must either get better at reproducing or cease to exist. Chance has nothing to do with it.