Effect of frequency on magnitude of photo current

In a photoelectric experiment, if the frequency of incident light is slightly raised while holding intensity constant, I understand that the number of incident photons decreases. This in turn results in the emission of fewer photoelectrons and thus a smaller saturated photocurrent.

While this seems to be a logical flow of events, I am slightly confused by why exactly the photocurrent would fall.

When the frequency of light is raised, the photon energies also rise. This allows for the emission of photoelectrons further below the fermi level. The distribution of electrons in metals would suggest that it is a fair approximation that the fermi level is indeed the highest occupied level at 298K.

As a result, the ability of the incident photons to excite photoelectrons is increased significantly. This would translate to a higher absorption coefficient due to the increased number of electrons that can be excited. A higher absorption coefficient then means that a higher number of photoelectrons can be emitted near the surface of the metal, translating to a higher photocurrent.

The question then is, what are the relative impacts of these competing effects and why is it generally assumed that the photocurrent decreases at higher frequencies of light?

I would guess that the energy band of metals is very narrow. Having a very narrow band would mean that any photons with energy well above the work function would not have a higher probability of exciting electrons as no electrons will be present at levels significantly below the fermi level (until the next quantum shell is reached)