Asymptote
Banned Idiot
No it's not an assumption, just laws of physics. You'll figure it out if you compare how fast you can run with how fast you can change the course of your action, the two measures are unrelated. Traditional theory of "the faster the better" had been replaced by John Boyd's energy-maneuverability theory decades ago, at least in regards to dog fights.
I won't argue faster climbing rate gives one advantage, however, it's a different measure other than supercruise, apart from relating to T/W ratio, for example, the wing configuration (in fact the the shape of fuselage too) offers different advantages to either capacities.
If I am not wrong, the energy-maneuverability equation goes like this :
Ps = [T-D]/W*V
Ps =Thrust - Drag / Weight * Velocity
So, velocity is a definitely factor, in fact, it is a multiplier. So a faster aircraft would have harder chance of turning because of the potential energy required is relative to the velocity (speed)? Is that what you mean?