@kregora Agree that would be ideal in an ideal world. However, it would need to be implemented in a way where performance is not overly degraded with large numbers of clients/players.
I know Battlefield uses Frostbrite (3?) but I don't know the extent that real time physics is implemented in that engine for Battlefield. I would like to know if someone authoritatively can add to this...
Generally, my understanding is that physics in multiplayer games (e.g. car racing, golf and other ball games etc), the implementations usually require the physics to be handled on a dedicated server, with predictive behaviour being interpolated/extrapolated at the client.
Some discussions:
https://gamedev.stackexchange.com/questions/35459/multiplayer-networking-with-physics
A description of implementation for Unity engine:
https://docs-multiplayer.unity3d.com/docs/advanced-topics/physics/index.html
General discussion on implementation and issues by developers on Unity:
https://forum.unity.com/threads/multiplayer-physics-game-where-collisions-between-players-is-the-core.685540/
For this idea regarding loadouts and movement speed/agility, I suggest it might be better to fake it. For example, as @DyeusVita suggests, a value is given to each item that can be carried. Add the items values and you have your loadout penalty that affects your speed and agility - walking, running, jumping, climbing, going up ropes, ladders, stairs depending on the activity. Nothing new there, just I don't recall it being implemented in Battlefield.
But I agree that it would add to the realism and gameplay.