You might be interested in the Starcraft 2 (SC2) league system. SC2 is a computer game where players battle in a 1 vs 1 real time strategy game where, just like in chess, the outcome is win, draw or lose.
To make the game more enjoyable for the players, the company behind it created a number of leagues (bronze, silver, gold, ...), in which players participate 4 seasons a year--although promoting and demoting works a bit different than in your proposal. The nice part is that, at any moment, you can just hit the "play" button and the automatic matchmaking system will find someone around the same strenght for you to play with, usually from the same league. Typically this takes a few seconds, and if not enough players are online it will broaden the search to higher/lower ranked players.
I haven't convinced myself that this will work on lichess, though. In SC2, leagues are the only way of telling how good you are; whereas here we already have ratings and you can easily measure your improvement as such. But it might provide some inspiration...
To make the game more enjoyable for the players, the company behind it created a number of leagues (bronze, silver, gold, ...), in which players participate 4 seasons a year--although promoting and demoting works a bit different than in your proposal. The nice part is that, at any moment, you can just hit the "play" button and the automatic matchmaking system will find someone around the same strenght for you to play with, usually from the same league. Typically this takes a few seconds, and if not enough players are online it will broaden the search to higher/lower ranked players.
I haven't convinced myself that this will work on lichess, though. In SC2, leagues are the only way of telling how good you are; whereas here we already have ratings and you can easily measure your improvement as such. But it might provide some inspiration...