Comprehensive list of Champion Skill Requirements (WIP)
I made a list using every champion in the game to try to clarify which champions require the most player skill. For the purposes of this list, I will be using the term "knowledge requirements" to describe knowledge of the game (for example, champion stats, cooldown tracking, resource management) and "skill requirements" to describe mechanical technique (for example, Insec'ing, Shurima Shuffling, or outplaying a combo using Fiora's Riposte). I will also be using the term "skill ceiling" to describe champion strength when mastered and "skill floor" to describe champion strength in a player's first few games. Skill tiers are ordered with highest requirements at the top and lowest requirements at the bottom, and then highest requirements in each tier are listed to the left with lowest further to the right. I am very open to feedback and encourage anyone reading this to leave comments with your opinions and suggestions.
TIER 1 (Highest requirements for both knowledge and skill. High skill floor means champion can't be picked up without dozens of games dedicated to learning them. Recommended only for those with a high amount of dedication to the game and the champion.)

TIER 2 (High requirements for both knowledge and skill. More than 4 abilities, abilities interact with each other in multiple ways, or numerous skillshots/high resource requirements. Kit can be very unforgiving, punishing the player for engaging incorrectly or misusing an ability.)

TIER 3 (High requirements for either knowledge or skill, but not both. High skill ceiling, but not necessarily high skill floor.)

TIER 4 (Median requirements for knowledge and skill. Skill floor is not far from skill ceiling, one or both are near the middle of the pack.)

TIER 5 (Low requirements for either knowledge or skill, but not both. Low skill floor, but not necessarily low skill ceiling.)

TIER 6 (Low requirements for both knowledge and skill. Some abilities have no active, abilities are very cut-and-dry with clear effects or simply damage, or few skillshots/low resource requirement. Kit can be very forgiving, providing the player with heals or second chances.)

TIER 7 (Lowest requirements for both knowledge and skill. Low skill ceiling means that with fewer than 10 games, a player can learn all there is to know about the champion. Recommended for beginners who haven't played MOBAs before.)

I want to close by stating some of my personally held beliefs. Champion skill requirements are unrelated to champion strength. Just because a champion is "easy" doesn't mean it's an insult to the champion or the player using them. Just because a champion is "hard" doesn't mean that the player using them is just better than the other players in their game. Different players have different specialties. Some players have a good sense of when to go in and who to focus. Some players have good accuracy with skillshots. Some players are proficient kiters. Due to unique player traits, different picks will suit them better than others, and other picks will take them more time then they are willing to commit to master them. A player who can get 80 CS with Swain at 10 minutes might feed on Riven because they have a strong urge to kite an enemy instead of engaging them. I recognize that this gives me bias as well, which is why I tempered this list by researching skillcaps at http://champion.gg/statistics/#?sortBy=general.winPercent&order=descend . This is meant to be a work in progress. Please bear with me as balance changes and champion reworks occur.
EDIT 1: Jhin added to tier 2. Shen moved to tier 2 from tier 6. Kindred and Twisted Fate moved to tier 3 from tier 4. Akali moved to tier 4 from tier 5. Ryze moved to tier 3 from tier 5. Master Yi moved to tier 5 from tier 7. Jax moved to tier 6 from tier 7.