Intermediary gaits where common 200+yrs ago then bred out mostly, why not show up more in reg gaited breeds ?

There are known "Trotting" breeds of horses that are thought to never have an intermediary gait, but, most riding horses of several centuries past were ALL easy gaited, if the trait is in the genes even way back, why couldn't those same genes or traits for easy gaiting pop back up from time to time.. I know of Arabians, Andalusians, who have a rare few members of PURE PURE horses that show obvious examples of an intermediary or broken easy gait. Could anyone add horses they know that don't come from a known "GAITED"breed, but show a different or four beat footfall pattern?