I don’t find this so strange. You can consider the F-14 to be the culmination of the Missileer idea: the concept first evolved into a part of the TFX program (putting the heavy missiles on the F-111B), and then after the F-111B was cancelled the missile technology moved to the F-14. But you can equally well consider it as a return to dogfighting: the Navy was considering a VFAX program to replace the F-4 and A-7, and this was partly driven by experience in the Vietnam that the F-4 was lacking in dogfighting. (The same experience that led to the creation of the Navy Fighter Weapons School/Top Gun).

It turned out that a single aircraft could fill both roles. According to George Spangenberg, who was head of aircraft design in the United States Navy’s Naval Air Systems Command at the time:

Since it was obvious to the Navy from the beginning of the TFX program that its success as a Navy fighter was highly questionable, the Navy continued its study efforts to find some means of procuring a weapon system that would handle the threat and be a successful general purpose, carrier based fighter. With OSD insistence on the F-111B continuing, the Navy looked at many alternatives. The F-111B was most nearly useful when employed in a fleet air defense role, in effect acting as a MISSILEER but with half the capability. Other fighter missions, such as escorting attack airplanes, had to be done with a higher performance, more maneuverable, and more versatile airplane than the F-111B. Grumman, associated with General Dynamics, had performed F-111 improvement studies, under contract, ranging from minor changes to complete redesigns. McDonnell had also studied, under contract, various improvements to the F-4, including a design with a variable sweep wing. A new airplane, to complement the F-111B, was also under study by everyone. This design finally evolved as a multi-mission airplane, VFAX, capable of performing better than a F-4 as a fighter, and better than the A-7 as an attack airplane. The concept was valid only under the premise that it was complementary to the AWG-9 and Phoenix capability represented by the F-111B. However, as the latter design degraded in attractiveness, by 1967 and 1968, very serious study efforts were undertaken to find a true solution of the Navy’s fighter problem. In essence, this finally evolved as upgrading the VFAX to carry the AWG-9 fire control system and the Phoenix missiles. The first definitive studies were completed by Grumman and provided the information by which the Navy convinced itself and the Congress, if not OSD, that a new fighter, VFX, could be produced which was more effective and less costly than continuing the F-111B and providing an adequate complementary fighter. 

So you can consider the F-14 as the outcome of two separate trends, and at the time of its introduction it was maybe the world’s best BVR fighter and dogfighter.