Actually there is very little stress on the cables. The cables are stressed just enough to take the sag out of em. i.e. All the cables are actually supporting is their self weight! All you need is a hand-held jack and a lot of clever math, to install them :-).
The deck on one side of the tower is held in place by counter weight of the deck on the other side.
About earthquakes, it's designed for those 100 year quakes, hurricanes and floods. When we were building the Audubon Bridge across the Mississippi River, we were in fact hit by a 100-year flood and 2 hurricanes. Other than some stored material floating away and having to watch out for alligators in odd places. We got through fine :-)
The bridge type is rarely chosen for beauty :-) especially when contractors have to bid competitively for tonget a chance to build them. Governing factors are technical feasibility (design and constructability) and cost.