Why is the classical model of light insufficient in explaining the photoelectric effect?

In the classical model, light is a wave and it's energy depends on its intensity. This would predict electron emission at all wavelengths of light. So the model cannot explain the threshold frequency of light required to cause photo-emission. However, in the quantum model light is made of small discrete packets of energy (photons), whose energy is proportional to the light's frequency. The one-to-one interaction between photon and electron means in order for photo-emission to occur, each photon must have a minimum energy, hence a minimum threshold frequency for light.