actually it does take the a5e breakdown. The numbers appear to suggest your statement is correct, but the critical caveat there is that those numbers are also calculated with no feats & no magic items. Simply add a +2 to the champion's greatsword & it inverts pretty quickly getting even worse when you add GWM. Sure you can add a +2 to any of the casters, but the important difference is that the champion multiplies the +2 & gwm by the number of attacks while the caster does not.In no way does 5e come close to inverting linear fighter/quadratic wizard. It would not even do so if every sword strike was lethal rather than the fighter wandering round effectively with a nerf sword (or a foam rubber cosplay sword) thanks to the nature of hit points, especially in 5e.
This is among other things because combat isn't everything - and in part because at both 1st and 20th levels the fighter's big thing is moving a normal move distance and swinging a piece of sharpened metal hard and fast. There is almost nothing other than an improved proficiency bonus that distinguishes what a L1 fighter can do from a L20 fighter in the exploration and social pillars.