For any plane to excel in one role, it almost always is worse in others. There is a running joke in aircraft circles that defines a plane as a series of compromises flying in formation. In the case of the interceptor all effort was put into making the plane be able to get into the air as quickly as possible, destroy the bombers just as quickly, and then land. If performance in the traditional fighter role (that is, fighting other fighters) needs to be sacrificed in order to achieve this, so be it. The result is that interceptors often look very impressive on paper, typically outrunning, outclimbing and outgunning less dedicated designs, yet they tend to fare poorly in combat against those same "less capable" designs.
Interceptor aircraft, in approximate chronological order: