The gas tubes respond in several microseconds. For AC line voltages, they will effectively be a short during each half cycle. If one doesn't have an inline fuse, both wiring and spark gap could suffer damage.
Varistors are the preferred device for use across AC lines but they have their own issues. If the surge event causes catastrophic failure of the varistor, it can catch fire and damage equipment. Varistors should have a thermal fuse in-line to avoid possible fire hazard. Three lead varistors have a built in thermal fuse.?