In the photoelectric effect, why is the kinetic energy of the electrons independent of the intensity of light?

In our situation, the stopping potential doesn’t let any electron to pass. When we increase the frequency of incident light, the electrons get more energy. We know it from equation E=hf. When electrons gain more energy they can overcome the stopping potential. In effect they can reach the point due to acquired Kinetic Energy. Intensity doesn’t matter in this situation, because stopping potential will eventually force every additional electron back. Intensity just makes more electrons. On the other hand, higher energy caused by greater frequency makes current decrease. Constant intensity causes electrons to be ejected at the same rate all the time. They have greater velocity thanks to frequency. There will be fewer electrons travelling because they will quickly reach the point and there will be a time gap until the others will come. The experiment setup is like a motorway and current measured is like traffic. When there are few fast vehicles, there is no traffic.