I've never heard that the S-turns were used to avoid flying over Chinese or Soviet airspace. The reentry burn is roughly 180 degrees longitude from the touchdown point regardless of where you're going to land. At that point, even if they were over the Soviet Union or China, they'd still be at orbital altitude.

The S-turns are used to manage the Shuttle's energy during reentry. The flight control computer monitors the Shuttle's progress during reentry and uses the S-turns to ensure that the Shuttle arrives at a certain altitude near the landing strip at a specified time before final approach.

Essentially, the S-turns allow for a certain "fudge factor" during the reentry. There's always variability in the Earth's atmosphere that has to be accounted for in real-time. You could change the reentry profile so that S-turns wouldn't be necessary by perhaps performing the OMS retro burn somewhat earlier. However, that wouldn't give the flight computer much in the way of margin to handle events as they unfold.

The Shuttle, especially when transitioning from supersonic to subsonic flight, has the glide ratio of an anvil. The last thing anyone wants is to be too low during the approach. Even more than conventional planes, it's extremely bad for a Shuttle pilot to be "out of airspeed, altitude, and ideas" on the approach.

Over the weekend, I heard one engineer describe how the Shuttles already use the most gentile reentry profile possible, so there wasn't anything the crew could've done to reduce the thermal and structural loads. His point was that flying anything other than the most gentile profile would add to the stresses on the vehicles and shorten their operational lifetime.