Quick fix (Lol.. it won't be quick) for all this fall damage from minimum heights would be solved with a drop feature. Allow the player to lower themselves from a high area (Walls, buildings, ect.) Just like they have a "Climb" feature. Allow the players to drop down from a height slowly like the climb up or jump off quickly and take damage as is now (Or fall off the wall).
Its realistic, would fix most of the griping about fall damage and bleeding, leaves the player vulnerable to enemy fire while taking the safer drop option. I don't want to see squad turn into "HARD CORE PARKOUR!!!" military bullshit but that's how I've gotten down walls with combat gear, Slow with security.
How to implement it? Sure as shit wouldn't use the jump key to initiate the drop. Could imagine the frustration from players leaping to their deaths when they wanted to drop. Probably a mix of crouching and looking down at the edge or some shit idk.
Lets beat this dead horse a little more, I think the meat isn't tender enough.