How I feel the rotation system should work
The free rotation system is something that has existed in League of Legends for years and years, and it's been exactly the same since the beginning. However, it becomes nearly impossible, especially for new players, to play every champion and see what they like. These ideas are primarily targeted at newer players, but can help veterans of the game who don't own all champions as well.
First off, all champions are available to players for their first week playing. This is to give new players a chance to try out as many champions as possible in their first week and get a general idea of what playstyle they want.
Second, there are 12 total champions on the free rotation, 2 from every main class (fighters, assassins, marksmen, supports, tanks, mages), one with higher skill cap and one that's simpler. Every week, 6 of the 12 rotate out and a new 6 rotate in, and then the next week, the 6 that didn't rotate out the previous week rotate out and a new 6 rotates in, and the cycle repeats. This way, players have 2 weeks to play free rotation champions before they rotate out, but champions rotate every week. Obviously, the first week will have to be rotating out 6 champions who were only in the rotation for 1 week. What this does is it makes the rotation serve as half suggested champions to play for new players and half harder champions for veteran players to pick up and start to learn before buying them themselves.