Weight distribution to the front in normal braking is because when stopping force is applied at the front tire/road interface, the entire car tries to "flip over" the front tire, a "moment" is created as the CG of the vehicle is slowed, but by a braking force (at the road) acting BELOW the elevation of the CG (which is above the road).
This weight transfer really helps, it allows MORE braking (backward) force, because the tire has more downforce against the road.
Whatever weight/force advantage is gained at the front is lost at the back - the vehicle isn't any heavier!
OTOH, braking only from the rear never gets this tire/road traction improving effect., the CG being in front of the braking force at the road.
Sarah! A great diversion back to reality. :)
And yes, I agree. You may rest your case. :)