Right behind the bumper, is the frame. If the push bar helps with that frontal impact, then you need the push/impact bar at the rear and sides.
The push bar in front 'helps' by protecting the plastic '5MpH bumper' structure in front.
The primary benefit is, even if the hood and the pushbar are damaged by a frontal strike, it's much harder to damage the radiator & condenser,
although not impossible. Basically, you're making the front crumple zone much tougher to crumple - they're frowned upon in Europe, for example.
(Europe basically looks to treat every pedestrian as blind people with near absolute rights to do whatever the hell, push bumpers 'get in the way' of that 'liberty'.)
The 2ndary benefit it's very helpful for actual pushing of other vehicles, and other stuff.
I've pushed other vehicles with my previous Caprices 9C1. The 9C1 with the pushbars made it MUCH easier.
And losing all 'give' [impact absorption]. I don't necessarily see that as a benefit.
The impact absorption 'lost', protects the radiator / condenser, by transferring that 'responsibility' to the other vehicle / object in question.
I know some versions are called 'bull' bars. I wonder why more of those people haven't spoken up yet ... ?
Being from NYC, I'd actually like to have the incredibly basically utilitarian NYPD-version of a push bumper installed on my Tahoe's front bumper.
Sticks out less than 4", with high durometer rubber pads making (intentional?) contact with whatever in front.