Mobs that are ridden and equipped with an elytra incur fall damage upon landing gently while under player control

Let's first clarify what controlling an entity means. Utilizing

/execute on controller

enables the identification of the entity's controller. You are the controller of a mob under the following conditions:

• For horses, donkeys, mules, zombie horses, skeleton horses, and camels, you become the controller if you ride it, the entity is tamed, and has a saddle.
• For pigs, you become the controller if you ride it while it's saddled and hold a carrot on a stick.
• For striders, you become the controller if you ride it while it's saddled and hold a warped fungus on a stick.

If you're in control of any of these entities and they're gliding with an elytra, they may sustain fall damage upon landing, even though they shouldn't.

Steps to reproduce with horse

1. Play in a flat world (just to make it easier to reproduce)
2. Run the following command while flying in the air:

   /summon horse ~ ~ ~ {FallFlying:1b,Tame:1b,ArmorItems:[{},{},{id:"minecraft:elytra",Count:1b},{}],SaddleItem:{id:"minecraft:saddle",Count:1b}}

3. Mount the horse
4. Glide with the horse slowly to the ground by not looking straight up or down
5. Notice how the horse wrongfully takes fall damage
6. Fly into the air again
7. Run the following command:

   /summon horse ~ ~ ~ {FallFlying:1b,Tame:1b,ArmorItems:[{},{},{id:"minecraft:elytra",Count:1b},{}]}

8. Wait until the horse lands safely

Observed outcome: When the horse is under player control via the saddle, it may erroneously suffer fall damage upon landing, whereas when not controlled, it lands without any damage, as anticipated.
Expected outcome: Regardless of player control, the horse should not incur fall damage when gliding in this manner.

Steps to reproduce with pig

1. Play in a flat world (just to make it easier to reproduce)
2. Run the following command while flying in the air:

   /summon minecraft:pig ~ ~ ~ {Saddle:1b,FallFlying:1b,ArmorItems:[{},{},{id:"minecraft:elytra",Count:1b},{}]}

3. Mount the pig
4. Hold a carrot on a stick
5. Glide with the pig slowly to the ground by not looking straight up or down
6. Notice how it wrongfully takes fall damage
7. Fly in the air again
8. Run the following command (same as step 2):

   /summon minecraft:pig ~ ~ ~ {Saddle:1b,FallFlying:1b,ArmorItems:[{},{},{id:"minecraft:elytra",Count:1b},{}]}

9. Mount the pig
10. Wait until the pig lands safely

Observed outcome: When controlling the pig with a carrot on a stick, it may incorrectly receive fall damage upon landing softly.
Expected outcome: Even under player control, the pig should not sustain fall damage when landing gently.

This issue may be related to issues like MC-269105 (more informative than the parent ticket). Relates to MC-14167.