I would think: Friction of the tires on the runway is proportional to normal force (the weight of the plane pressing down on them). At the beginning of the landing run, there is still substantial lift from at least part of the wing, even with spoilers deployed, reducing the effective weight on the wheels, and thus the friction available for braking.
Therefore, a rate-based autobrake system just won't have enough braking to work with, until the plane slows enough and puts enough weight on the wheels. Reverse gets you down to a speed where the brakes become fully effective, in less time and thus in less distance.
At which point the autobraking will give a constant rate of deceleration (if so designed), based on the combination of reverse thrust (if used) and friction braking.