Parasurama took incarnation to kill the evil Kshatriyas. There were innumerable kings during his period. They did not adhere to any laws of a Kshatriyas and were ruling as they wished. As there were many evil persons in the guise of kings, there was a need to destroy them
The kings who belonged to the Chandra and Surya lineage were ruling the kingdom as ordained and they continued to rule. Parasurama killed only the evil kings who did not let the virtues to flourish.
There is an elaborate explanation in Daya Shatakam with regards to this. Please click the below link to further your knowledge.