I am just back so I will write something.

You wrote quite a bit on what the "skill" of league of legends might be, and I didn't see anything in that part of your post fundamentally wrong. You probably cannot describe all of the skills that go into being a great league of legends player in one post. However, as I said the question is not what the "skill" of a player is but how MMR systems work.

When you have an MMR system this is designed to measure the skill of some team or individual relative to all others of the same type. When you have individual player playing an indivudual game like chess what is required is a relatively small number of games(in comparison to an individual in a multiplayer game) for that individual player to become confident that they are at "X" skill level in chess. When you have an individual player who plays a multiplayer game what is required for an accurate measure of that players skill level is for that player to play a relatively large number of games compared to the "game for individuals", player.

I presume you can check the claims in this paragraph out - but there is a ton of videos on "elo-hell" explaining why there is no such thing. If you have played enough games the only player holding you at your current rating is you. This is because you are the constant being measured. Whatever it is that constitutes "skill" in league of legends overall will over-time be measured accurately with respect to other player providing enough games have been played.

Now when you start to gain rating in a group of players what begins to be the constant being measured? Let us start by considering the case of one group only. It should be clear that the constant being measured is the group. The MMR system has no means to apply rating to the individual in the group simply because of the fact that rating gained is down to a different constant. This new constant being measured by the MMR measurement system is the group that gains or loses rating, and not the individuals.

The system has no means to measure the value of group synergy, no means to identify the shotcaller in the group - which the very best groups should have - no means to identify the weaker players in a group or the stronger either for that matter.

Let us consider further the very best group possible where each player in the group has equal skill - lets call this group - Group A. Let us suppose further that they face other groups of equally skilled players to them - which you can clearly see is the ideal situation. But wait, Group A smashes every other group they come across. Why would this be possible? Well this group knows each other very very well. They played together far more than the other groups, and have figured out how to play together and even though one of the group tilts easily - he gets untilted by his good team-mates. So a bunch of groups of equally skilled players get smashed by another group of players of the same skill level. This should make it clear that there are properties of groups that do not belong to the individual. So even in the perfect case where groups of equally skilled players play together, there are still factors that will effect the MMR system's ability to measure the individual.

Let us further consider the player who plays in a lot of groups. You might say that they are the "constant" in the groups.

However, this ignores the following problems and possibilities.

First, there is still no accounting for group properties like knowledge of team members, synergy/planning etc from any of the groups you play with.

Secondly, no way to measure your standing within the groups you play with. Are you the worst, below average, average, above average or the best player in your groups. What happens to every player is that their rating will tend towards the average rating which belongs to the set of groups they queue up with. This depends on the quality of the players themselves and the quality of the groups in terms of synergies within the groups developed overtime.

Fundamentally, rating gained through groups(s) is not individual achievement. This is why riot admitted from the beginning that the system isn't a measurement of individual skill.