Advantage of rotary spark gaps in tesla coil design
Rotary spark gaps are self-quenching, since the gap is only small for a very short period of time. 

Also, a rotary gap is significantly self-cooling, since one half of the gap is rotating at a very high rate.

Last, and probably most significantly, a rotary spark gap basically lets you control the arc rate, since you generally only get one spark per gap closure. Therefore, you can control the repetition rate by varying the rotor speed.