You're not thinking in the load axis. For a bridge, it'* vertical. For our purposes, it'* horizontal. The force applied is in a different axis. But the same load bearing procedure applies.
Let me try to explain it in simpler terms:
On a bridge, the load is vertical. It needs to support the load (weight) of the cars, and oppose gravity.
On handling for the car, the swaybars and strut tower bars come into play on LATERAL loads, or cornering. The more you stiffen it laterally, the better feedback or stability you get in cornering.
It'* the same principal, but 90 degrees opposed to a weight-bearing design.