Selecting something at random can be done for various reasons.
We are curious, and think we know ourselves very well, so to give up a choice to "random" factors outside our control is a bit thrilling and satisfying.
Randomness has been used in rituals through many cultures. To predict events, evaluate personalities, etc. Sometimes, randomness is seen as the Will of a God or of Spirits. Random occurences are said to be manipulated by ghosts.
Even without this supernatural explanation, randomness is used, Sortition, Cleromancy, Rule by Lot, have been practiced to ensure "blind" selection in some cases, which can be more fair.
The value of randomness is in its unpredictability, which stems from not knowing what caused a specific outcome.
Randomness, then, deprives us of knowledge. Therefore, randomness also gives us a thirst for knowledge. This is the Pedagogy of Randomness.
Randomness offers us a challenge, as "reasoning" creatures, we want to find underlying logic, our instinctual response to randomness is that there MUST be a trick, there MUST be a way to find out why, how. So, Randomness can keep us endlessly searching.
Some neurotic people hate randomness and chaos in every way. They want things to be predictable and logical. If they operate only in the world of Logic made by Man, they might succeed very well in it. But once they have to face the messy, illogical universe, with its black holes and hurricanes and radioactive decay, they will cower in fear before the power of Chaos.
Yet other neurotic people think they can control randomness, or believe that they can predict it or bargain with it, or, they might find that randomness is a tool of manipulation, that they can use it to make people addicted like gamblers, or use it to strike fear into people. They do not respect the universe, think they are masters of it.
Randomness is the fundamental Technology of the Universe' Will. By throwing sticks of the I Ching, rolling dice, drawing straws, watching cracks form and water flowing, we become connected to the Universe' Will.
Einstein said God does not play dice. Neils Bohr said, it does not matter if he does or not because we will never know if he does or not.
Randomness teaches us to desire knowledge, it teaches us to appreciate accidental occurences, to humble ourselves before the chaotic universe.
Randomness also teaches us to be wary of extremes, and to appreciate the calm and quiet. When a cacophany of noise gives way to silence, when a rush of waves becomes still, when the flames die out or the ice melts, we are thankful to find ourselves in the middle of the bell curve, and to have a break and give up control for a bit. And to remember how lucky we are to be able to control what we can.