It all comes down to efficient use of the time you have available to you, recognizing your individual strengths and weaknesses, and of course genetics.
Will building all around high degrees of athleticism (strength, speed, power, mobility, balance, endurance, coordination, agility, etc...) likely benefit any athletic endeavor? Yes.
But will the time it would take to reach very high levels rather than spending that time developing the combat specific skills to be able to apply that athleticism be worth the return on investment? In most cases of limited time and energy availability and mere mortal genetics, probably not.
Sport specific conditioning (pad work, bag work, shadow fighting, drilling grappling techniques with and without training partners, etc...) is going to produce the most movement specific athleticism as well as the crucial mechanical skills, timing, judgement, speed, and accuracy necessary to apply those skills effectively when it counts. Any time and effort spent on additional athleticism would be best spent on preventing injury first, addressing weaknesses (depending on the athlete/fighter) second and on just general athleticism if there is still available time and energy.