We need to go back to this style of punishment:
Yes, you can jump and shoot, but it is heavily penalized in Battlefield 4. You cannot aim down sights (ADS) or shoot at the start of a jump. Bullets spread wildly and the game applies an accuracy penalty if you rely on shooting mid-air from a standing jump
This is what they said as developers said in the past:
DICE and EA developers have actively responded to bunny hopping in Battlefield games. They stated that "CoD-like" movement mechanics—such as uncontrolled, momentum-retaining bunny hopping, slide-shooting, and jump-shooting—do not belong in the franchise.
Yet we have this in this battlefield.