It seems crazy that it doesn't apply to civilian vehicles too
It does but it only gets enforced for new vehicles. See the rear bumper mods that were required for the Mercedes G-Wagen 4x4 Squared. Note that federal regs prevented the activation of the LED aux lights for these as well.
The problem is that most of the inappropriately-tall consumer vehicles get that way after the fact. I.e., people modify them. If this is only getting enforced at the manufacturer level, instead of the vehicle-inspection level, it's not going to accomplish much in that category.
Passenger vehicles don't need a Mansfield bar, because their primary crash structure has to be between 16 and 20 inches from the ground.