particle physics - Photocurrent's dependence on frequency

Sounds like a rookie question, this, but could someone please explain to me why doesn't photocurrent increase when we increase the frequency of the incident radiation? I mean, an increase in frequency would mean that the photons would have higher energy (E=hf) and this increased energy should correspond to the emitted photoelectron. Now since photoelectrons have higher kinetic energy, they would obviously have higher velocity and since they'd have a higher velocity, then acc. to this formula, I=nea(vd), the current should increase but it doesn't (at least, that's what's written in my school textbook). It'd be great if someone could please explain this to me!

Edit: I didn't assume that a higher frequency would knock off multiple electrons. What I am asking can be explained like this. Let's say, for simplicity, that the photodetector is a kilometer away from the photoelectrons, and it shows the current as the number of electrons which reach it each second. Now, let's take a case in which, say, the radiated light emits a total of 10 electrons from a given photosensitive material at a given frequency and intensity, 5 with a velocity of 1 km/s and the other 5 with a velocity of 500 m/s. Obviously, after a second, only 5 electrons would have reached the photodetector and it'd show the current as 5 electrons per second. Now, in another case with the same apparatus, let's increase the frequency of the light without changing its intensity such that the velocities of the emitted electrons roughly double. Even though the emitted electrons are still the same, he velocities of the electrons would now be 2 km/s for 5 electrons and 1 km/s for the other 5 electrons. Now, obviously after a second, all the 10 electrons would have reached the photodetector as compared to only 5 when the frequency was low, and the photodetector would show the current as 10 electrons per second. This certainly contradicts the fact that photocurrent is independent of frequency (given the frequency is above the work function of the photosensitive material) so what I'm asking is simply how to explain this contradiction.

Thank you!