I think the main difference between the classical toy model and the quantum case here is that in the quantum case we have a quantization making it that not all orientations are allowed leading in discrete energylevels while in the classical case all orientations are allowed resulting in the continuous energydistribution. If we would have a quantum system with a really high nuclear spin, we would have a lot of different splittings and if the energydistances between them would be small enough we would approximately reach a continuous energy distribution again.