Don’t you ever get tired of fights you know you’re going to win?
— Spike, “Fool for Love,” Buffy the Vampire Slayer season 5 episode 7
You see an interest in randomization at the top end of the skill curve as well as at the bottom. If the optimal level for fun and learning requires a balance of the predictable and the unpredictable, you run into problems when mastery means a lack of uncertainty. You know exactly what is going to happen, you know you are going to win. As much fun as winning is, people get bored of “too easy” games and move on. Dunking on noobs is bully behavior.
Sometimes the purpose of randomization is to lower the skill ceiling. This helps avoid the near-certainty that the best player will win. Most people other than the best player like that, but the best player can also enjoy the lowered certainty. Even if it is not more of a challenge, because there is nothing you can do to be better against a lowered skill ceiling, it at least is not a trivially obvious win. There are better and worse ways of doing this, but sometimes throwing in a bit of chaos “makes it interesting” again.
Sometimes we want a bit of variation in the game not so much to lower the skill ceiling as to change the starting state and prevent the boredom of a “solved” game. That is, maybe the game is still solved, but with a variable starting state, you need to know a much larger and more complex algorithm to solve it, and with sufficient variation few people can keep that much in their heads. So you vary the starting position of pieces, vary the goals, vary some intermediate steps. You can still play a strategic game with perfect information but have lots of things that might play out differently. Games like Dominion and Kingdom Builder have fixed rules but variable components and goals, so you need to adapt each game to the goals, map, etc. A fixed game has fixed strategies, and the most experienced player already knows them all. A variable game lowers that advantage in a way that is fun for the veteran, without creating problems for new players for whom all configurations are still new.
Sometimes that variation is there to create a question in how you win, rather than whether you will win. This is an appeal in rogue-likes. The ideal is still that every game is winnable (some designs fail this), but you might need to vary your approach dramatically based on how things go this game. Even if you know you have a very good chance of winning, it feels uncertain when you do not know how. This can combine with true randomness, giving you things to react to along the way that were not predictable.
Certainty can be as un-fun as undifferentiated chaos.