Why would one need to take the shift in CoP into account?

Do get a more realistic representation of what is happening in reality perhaps?

You made a good and valid point, by pointing out that my shown calculation is based on an too simplified model.

To get 3g deceleration, one would need to take aerodynamic downforce into account - I fully agree with this and you are right.

You propose another model, with added downforce, and this model shows, that the effect of the load transfer is diminishing, because it becomes less significant when considering higher vertical loads. There is nothing wrong with this either, but this model is based on the assumption that the downforce distribution remains static (CoP doesn't move) during braking.

And I'm not convinced, that this assumption is correct/applies in practice - that's all, an the reason I mentioned that one would then also need to account for the CoP movement and the effects it causes. Otherwise we replace on oversimplified model (my initial), with another oversimplified model (your model assuming a static CoP).

It's not an F1 car, but I would expect a similar behavior in principle (as in CoP shifts under braking/pitch), which should help to show, what I wanted to point out, that CoP tends to shift forward under braking in most cars.

or in absolute values, for an more F1 like vehicle model.

Front downforce tends to increase with a reduction in front right height, which will cause a shift in vertical wheel loads, balance and CoP.