Aaaaand back to the circle...I don't agree with the loading. Your tieing max brake force being directly portion to load it's not
Unless your rear is off the ground you don't have 100% of the load on the front.
If you start with 50/50 and add rear brake would it not be more like 65r/35f
Braking with front or rear brake causes deceleration, and deceleration causes load transfer, and load transfer increases load on front.
Brake/ Deceleration > Load transfer > Increases load on front
Simplified model does not include engine brake, drag, rolling resistance, etc.
If you start with 50/50 and add rear brake 0...max, then load will be 50...33.3% r / 50...66,7% f.
That is also the reason why rear brake has only max 33.3% (0.33G) of the "stopping power" what front brake (1.0G) has.
That is why stopping distance (100-0 kmh ~120 m) with rear brake is three times longer than with front brake (100-0 kmh ~40 m).
Do you agree?