I seem to recall that most of the damage done to the Tristar was from the second bounce and not the first impact from the "auto land".
Following the first arrival and bounce, the crew applied a large helping of nose-down. The Direct Lift Control (DLC - very clever in its day) correctly interpreted this as a need to increase the RoD whilst also trying to hold the attitude, and deployed most of the spoilers - inevitably resulting in a much harder arrival than the first!