Not something that can escape the scope of early development and definitely not something too grandiose that would be overwhelming for a small development team. My suggestion is to implement a running feature the player can perform while crouching.
Crouch running wouldn't need any additional keys assigned for functionality, just the crouch key to crouch and using the sprint key while crouched. It provides the player a smaller profile when moving up to that next piece of cover. Allows their teammates to fire/suppress the enemy in the general direction of squad mates moving up by shooting over them more easily or when having to cut between crossfire (obviously there is always a risk of friendly fire though).
Not strictly a beneficial thing as the player's extremities are more centered, which can be an issue when receiving accurate incoming fire and I would also suggest it being slightly slower moving and burning slightly more stamina than a stand up sprint. So there is a small meta risk/reward factor in the mechanic. Obviously bound to the limits of inertia if the developers go that route in the future (slower animation, no "whack-a-mole" toggling). I honestly think it would fit very naturally into the gameplay and add some variety in movement under fire options.
Few games out there embrace this feature which should be a standard by now, in my opinion, especially when considering the tactical open nature of the game's direction. Red Orchestra franchise, ARMA 3, and Gears of War (Hence the moniker "Roadie Run*", though obviously not as rigid or abusive as it is in that particular game) all implemented variations of this type of feature with great success. Would love to see it in Squad.
*Named after the way roadies, or stage workers, quickly dart across stages during rock concerts, the roadie run is a fast, low to the ground trot performed as a way to avoid hostile gunfire.