War Saddles and Stirrups prevent riders from falling, if they are in a proper military saddle. This is consistent with history and video games.
Besides, even with PS 5 or 6 I am able to one shot any rider with a 2Her or Polearm due to the high speed that they are able to travel towards me with. Pointless if I kill them, on the small chance that they do survive (which is extremely rare) I say let them keep riding as a reward.
No to the idea, as I see little that would add to game play if this was added.