Indeed a very far fetched statement from you as expected. Cannons were NEVER a replacement for missiles even if they run out. It maybe the secondaring use of the cannon's but only a fool would think "hey im out of missiles, im switching to guns!".
In WVR combat If the target is less then a kilometer away, then missiles are deemed as in-effective as they cannot reach their terminal performance in that short period. This is exactly what happened in Vietnam war (which was fought 40 years ago and still you donot want to learn anything from it because you are too busy defending your vague and insane statements) when the F-4s lacked inbuilt cannons and the pilots became dependent upon missiles which were largely ineffective due to the small Migs slipping through beneath while they used their own CANNONS to down the large Phantoms. The combat kills of USAF vis a vis Russians/Chinese were reduced to 3:1 from 8:1 only because of some one like you perhaps made a blunder while designing the F-4 Phantom.
Nothing fancy