Disclosed are methods and systems for a user equipment device (UE) to avoid being served by a base station that experiences a threshold high extent of change of the base station's coverage identifier. In particular, the UE may detect a threshold high extent of change of a coverage identifier of a first base station, and may responsively configure itself to avoid being served by the first base station. In this way, if the UE is being served by the first base station, then the configuring may cause the UE to trigger a handover from being served by the first base station to being served by a second base station. Whereas, if the UE is not currently being served by the first base station, then the configuring effectively blacklists the first base station, such that the UE avoids attaching to and/or handing over to the first base station in the future.