You shouldn't even want to accelerate immediately at the same rate as the car in front of you, unless you're very optimistic about 1) having instant reflexes on the brake pedal even though your foot is currently on the gas pedal, and 2) your car's stopping distance being exactly the same as every other vehicle.

Having a time delay on your acceleration means that your following distance will increase as speed does, which is the safe behavior. I've had plenty of times when I thought "woo, we're accelerating, it's the end of the traffic jam!" and then had to hit the brakes when we came around a turn into more traffic. Traffic might be reduced if we all rode everyone's bumper all time time and accelerated as a single unit, but that doesn't mean we can actually do that without tons of collisions.