There is so much CC in the game at this point, that it's pretty much mandatory to have diminishing returns on Chain CC now. Nothing is more frustrating that not being able to play the game when you are literally CC'd to death for 5+ seconds.
The answer for this problem is simple, the first CC on your character has full effect. The second is half duration. For the 3rd CC it will have to come down to experimentation and balance. The 3rd can either be 1/4 duration or you become immune at that point for 3 seconds. Regardless, once you hit that 2-3 mark, you get CC immunity for 3 seconds. This allows for actually counterplay when you are the carry for your team.
So, for the love of God, please seriously consider taking the game into that direction. Otherwise, shorten all CC across the board, which of course would require every champion with CC to be balanced. So my idea is way less work and impact on the game. As for the argument that some champions have to be CC'd to beat them, that's where those champions need some reworking. CC should NEVER be mandatory to kill a champion.