The idea of Runes and Masteries, (And now the upcoming merged system with the newly announced "Runes Reforged") add a form of complexity and customization to League of Legends. If this didn't exist as part of the game, LoL would simply be another "Ho-Hum" MOBA in an ever-growing genre of video games.
As Riot themselves say, it allows players to create personalized playstyles, form strategies with the champs they like and counteract the strategies of their opponents, in certain cases.
They give the game a sense of "depth" that I feel it would not otherwise have. Removing them outright would leave the options of customization vastly decreased, and the player would feel far less inclined to put time into it.
The only things of which I know that players would still be able to choose:
- The champ they play.
- The skin of the champ during the specific game they play said champ.
- The Chroma, if applicable to the champ and the skin of the champ.
- Their name when creating a profile.
Other games are praised when they provide "depth" via customization, why can't LoL have it too?