Reproduction steps:
1. Create a new 3D project
2. Open Unity > Shortcuts
3. Under "All Unity Commands" find "3D Viewport/Fly Mode Backward"
4. Double click on Shortcut - "S"
5. Press Down Arrow on a keyboard

Expected result: Shortcut changes from S to Down Arrow key
Actual result: Shortcut doesn't change to a Down Arrow key and stays S

Reproducible with: 2020.2.0a16, 2020.3.17f1, 2021.1.0a1
Not reproducible with: 2019.4.30f1, 2020.2.0a15, 2021.1.0a2, 2021.1.19f1, 2021.2.0b9, 2022.1.0a6

Notes:
- On Windows instead of a second step go to Edit -> Shortcuts
- In all not reproducible versions Editor shows Binding Conflict warning - "The key ↓ is already assigned to the "3D Viewport/Fly Mode Down" shortcut. Do you want to reassign this key?"
- If you change "3D Viewport/Fly Mode Down" from Down Arrow to any other key and then try again to assign the Down Arrow key to "3D Viewport/Fly Mode Backward", instead of assigning it correctly, it will assign this key back to "3D Viewport/Fly Mode Down"