Doubt on the predictions on the photoelectric effect according to the wave theory of classical physics

Presumably you know that experiments demonstrated the falsehood of the Classical model.

The model was based on the simple idea that the more energy you hit the electrode with, the more energy it would give each electron. Light was treated as a wave of such energy.

In that model, it follows that greater wave amplitude (light intensity) would impart more energy to everything it hit.

It is less obvious that a shorter wavelength carries greater energy than a longer wavelength of the same amplitude. It has to do with the rate of change of the wave form (the slope of the curve when you draw it), and is true in both the classical and quantum models.

However I am unclear why shorter waves should be expected to increase the current, as that is the number of electrons not their energy. Perhaps it is because there are more peaks per second, which would supposedly therefore knock more electrons out.

Of course, we all know that experimental observations gave the lie to all that. Einstein explained it as energy thresholds, by treating the light as discrete particles or packets, and in doing so co-founded quantum physics and earned himself a Nobel prize.