There were quite a few fighters from the '50s that carried rockets as a primary armament for air-to-air combat, like versions of the F-86, F-89, Some YaKs (IIRC YaK-25 maybe?) etc. The M3e.262 carried rockets for use against bombers, and some German fighters carried mortar launchers for the same purpose. Granted these were intended for use against heavy bombers, but the concept is not unknown.
Damon.