i disagree.
The idea that a game can't be fun and fair is ludicrous and very subjective to say the least.
Fun can be found in a variety of ways and it's all about personal preference.
there was a study on "gamer" motivation. the study found that the primary contributing factors to gamer motivation are competitiveness, social interaction, and entertainment through the values of roleplay, puzzle-solving, storytelling, and stress-relief. There are a few other minor nuanced factors, but these are the primary ones.
Fun is the word that one uses to describe the relationship between an action and an emotion. Emotions are caused by sensations in the brain and nervous system that are controlled by chemicals in the body and then relayed back to the brain through nerve receptors. Over time the brain attributes actions with beneficial, harmful, and neither.
When our brain identifies something as being beneficial and our body has to perform very little effort to maintain that action then our brain tells our body to release chemicals to indicate that the action is fun.
Therefore, the entire process of defining something as fun is arbitrary.
The process for defining something as fair is similar, but based on social and cultural construct. Is this action more beneficial to me than others? is this action more harmful to me than others? Is this action neither?
our brains relay that something is fair when it's neither beneficial or harmful, but what is determined to be beneficial or harmful is unique to every person. This creates the variances of what is considered fair and unfair. It's also why as a society we try to educate our children to behave in a certain way and to understand and experience things in a certain way.
enough about proving that your opinion is subjective.
on with proving that something can be fun and fair and that by losing one can still have fun.
Timmy desires the social interaction from Bethany because Timmy has hit puberty and is looking for a mate due to the chemical responses in his body telling him that he's ready and it would be beneficial to do so.
Bethany is taking hormonal birth control suppressants because her mother tells her it's the right thing to do. This has caused her to become aggressive and ignore her natural sex drive due to the chemicals in her body. What she does enjoy, however, is the chance to insult someone else and prove that she is superior to them due to her lack of control over her life having been categorized by her brain as harmful.
Alex a gender fluid female has spent countless hours learning how to do math on the fly and spends most of her day socializing on the computer and for fun she spends time pretending she's someone else. Due to her high grades and slender form she is highly respected by her peers and so her brain has taught her that she is just born awesome. Everything begins to bore her because it's not creating enough of a challenge and through her father's oppressive disciplining she has developed a belief that only by being challenged can one improve.
Timmy and Bethany end up on the opposite team from Alex. Alex is roleplaying as a fierce rengar and is amusing herself by going off-meta build. She still dominates of course and so she becomes dissatisfied and bored. Timmy is doing poorly with his duo friend Bethany, but he's just happy to have her company. Bethany on the other hand is irate. Her bottom lane teammate keeps telling her how to support and she never liked supporting anyway. She hasn't bought an income item because she thought the stupid ADC would help her get first blood. instead of playing a standard support she's opted to go brand with a dark seal and plans to build rylias later to compensate. Timmy Suggests that she come mid to join him because he's doing poorly against this crazy OP rengar (alex). To him this is an easy opportunity to show Bethany that he's not bad at the game and besides. He had queued ADC anyway. They were supposed to be bottom together in the first place. Bethany goes mid and starts flaming her ADC in chat telling her opponents to report their bottom laner for "being toxic" and then continues to talk in all chat about how she's going mid and not helping bottom. While mid Bethany manages to get a few kills on Timmy's lane opponent and starts trash talking Timmy's lane opponent in all chat. Alex having already calculated the max damage output of brand knows that she can't kill her currently and decides to go top for her final stack on rengar's passive. Unfortunately for her she is up against a singed who keeps throwing her away when she dives him. She ends up going into chat and while pretending to be rengar she starts referring to singed as her prey. Alex stops worrying about the game and becomes fixated on the idea of killing singed while Bethany snowballs out of control in the mid lane and helps Timmy turn his 0/10 yasuo into a winning game. Timmy calls Bethany his babe while Bethany takes to the all chat to inform everyone on the enemy team about how much they suck. Alex got her final stack at the last moment when singed got stuck between the turrets of their base. She flashes her M7 rengar icon and during the end game screen she once again imitates Rengar even going so far as to repeat the words she's typed in her room to herself.
Who had fun?
The answer is supposed to be that all 3 had fun. Timmy got to spend time with Bethany, Bethany got to prove her dominance and independence, and Alex was challenged even though she lost.
However, your theory that league can't be fun and fair at the same time is still important because that means you feel that way. This is a side effect from your own personal experiences as a player. Your brain has taught you that you're only able to have fun while winning. That the only benefit of this game is to win. This is a problem with the Esports gaming community and not necessarily League of Legends on its own.
If you would like to discuss the issue feel free to let me know.