In most jurisdictions, bumpers are legally required on all vehicles. Regulations for automobile bumpers have been implemented for two reasons -- to allow the car to sustain a low-speed impact without damage to the vehicle's safety systems, and to protect pedestrians from injury. These requirements are in conflict: bumpers that withstand impact well and minimize repair costs tend to injure pedestrians more, while pedestrian-friendly bumpers tend to have higher repair costs.

Can we conclude that does a car have to have a bumper?
yes