No. Rapid acceleration from being rear-ended causes whiplash. Having brakes on reduces the initial acceleration.

In modern bucket seats the risk of whiplash injury is incredibly minimal. Your head doesn't have the distance to travel far enough to hurt your neck. On the other hand, standing on the brake will cause both vehicles more damage and cause the other car to decelerate more quickly, causing the occupants to experience more acceleration in a direction in which the restraints are less effective (getting pressed into seat-belts and airbags hurt more than getting pressed into a seat).

Standing on the brake is simply shifting the energy around at the expense of the other party

If there is a car in front of you, not holding the brake is shifting energy at their expense!

Assuming an intersection, wouldn't it be better to be rear-ended hard than having a vehicle slam into the driver's side door?

Yep, which is why I think it depends on what's in front of you. A human probably doesn't have enough time to analyze the situation and determine whether or not they could do better than holding down the brake. A computer can probably do better in some situations.