Making build decisions based on what is the most mathematically effective balance of damage, crit, attack speed, and armor penetration is perfectly fine for maximizing the efficacy of your champions, but it's not super fun.
That's already what we're doing. It's why IE + SS is purchased so much now, but in the past BT was always the rush item and it was very often followed by Last Whisper. People make choices based on expected dps, not any love for crit. If crit gets nerfed, it will not be bought, no matter how "fun" it is. Mathematical choices already reign supreme.
there is the chance that they have the item active cooldown reduction, or other such things - you do not have full visibility of your opponents status at all spheres of the game. This game has a large degree of hidden power.
I can look at runes and masteries before a game starts, and I can make choices about controlling vision through warding. I have some way to interact with both aspects. Neither are like crit.
Why is a dash->zhonya's->flash->dash combo form of survival acceptable, but a 3-in-a-row crit kill not? Whether an effect is chance based or activated, why does that matter in the overall scheme of "your failed gank" or "your failed engage?"
Because one is a player using skill to achieve a specific outcome (they have to actively choose to use every dash, zhonya's, whatever else), and the other is flipping dice. In a game based around skill, one is a desirable way for interactions to occur, and the other isn't. Easy as that.
Your standard for evaluating the fun-ness of randomness seems entirely arbitrary.
Then let me make it very clear: anything where players and their interactions are not deciding the outcome is not fun, because it takes away the only point of playing the game. RNG is a system where random numbers decide the outcome of a fight instead of players. It is therefore undesirable. If the starting postulate "player interaction is good" is accepted, then this really isn't an arbitrary standard. Additionally, many of the things you call "random" are actually just "hard to predict". Big difference. One is the result of another player doing something.
You assume that because I can't control the actions of another player, those actions are "random". This is where you are wrong. Those actions had decisions behind them. Choices were made, and I interacted with another player through them. It is deliberate, not random, even if I fail to recognize the other player's actions until I have already lost. In crit, the deciding factor is a roll of the dice. The outcome is not determined fully by the players unless there is no variance. Randomness is involved and can determine the outcome.
Is it somehow more random than an Ezreal ult flying from the jungle to blow you up because it came off cooldown five seconds earlier than you anticipated?
Yep, because I could have anticipated that. I could have warded to see the Ezreal, or noticed that he was missing, or flashed it, or known the cooldown better. I could have always done something better, and I can use that to improve. I can't anticipate streaks of RNG, because it is always a better option to play assuming standard ranges of variance. There is nothing to improve. There is nothing to think about. It's boring in the extreme.
This, like the RNG, is a random element completely out of your control, yet you are able to tolerate their existence in the match.
They are necessary for the game to exist. Crit isn't. I can't have a team game without teammates. I can have an AD steroid without variance. Also, being hit by Ezreal ult isn't completely out of my control, as I've said earlier.
Your ability to win or lose is already largely out of your control, due to the presence of 9 other people in the match all taking various actions of a sort.
This is irrelevant to me. I am playing a team game. By necessity, teammates determine victory. I don't care about that. Victory vs defeat isn't something I care much about. I do care about whether the gameplay is fun and engaging, and this is an aspect that is neither fun or engaging. If you want it put in terms of "control", then think about it like this: while it is a necessity to have teammates that can influence the game in order for the game to exist, it is not necessary to have RNG that can have any control over the game. One is needed for the game to exist. The other isn't. Completely separate.
You will have more fun if you accept that and embrace the glory of randomness. Accept the blessings of the RNG.
Can't happen. If there is going to be randomness in a game, it should always be in a way that allows for player interaction. If that isn't fulfilled, it's an inferior game mechanic. Purging it would be much more enjoyable than acceptance.
Finally, a small request. If you are going to quote large sections of my response at once, please feel free to just quote the beginning and end points to save space. We are beginning to take up a lot of room on this thread.