K2-SO aside, we only see other KX-series droids in imperial service on-screen inside the base on Scarif. This base was completely destroyed. While there isn't enough information for a concrete answer, the destruction of this base, and the method of such destruction can be used to explain the lack of appearance of many things found in the Rogue One movie that were not in Episode IV. (i.e. Tie Stryker, U-Wing, Many different Troopers, etc).
Also, the official starwars.com databank describes Scarif as "the principal construction facility for the vast Imperial war machine." It is possible that the destruction of a large portion of the planet also destroyed any manufacturing facilities for these droids.
Additionally, there are very few "Imperial Bases" that we visit throughout the original trilogy. All we know is that we have not seen any KX-series droids in service on Star Destroyers, or the Death Star, but that is not a large enough sample to assume that they simply do not exist during the Original Trilogy.
EDIT: For completeness. After rewatching the movie, we also see a KX-Series droid in service inside Jedha City. However, since this location was also completely destroyed, and the one we saw in service was terminated, I think the rest of my explanation still stands.