1. The LM358 has a relatively low gain-bandwidth product. Its maximum open loop gain decreases with increasing signal frequency. Basically, for any particular closed loop gain in a circuit, the response is flat up to the point when you intersect the open loop frequency response curve, at which the amp acts like a single-pole lowpass filter. For a gain of 100, this happens at around 5 kHz. So while the zener noise might be very wide band, the output amplitude of U3B will roll of starting at around 5 kHz when observed with a spectrum analyzer This will have the effect of reducing the high-frequency content of the noise going into the comparator. Out of the comparator, the number of narrow pulses will be disproportionately lower than the number of wide pulses.
2. Try the circuit with no hysteresis around the comparator. Hysteresis removes transitions due to low amplitude parts of the noise signal, another way of low-pass filtering the result. Delete R4, R5, R8, and RV1, and tie the pin 3 comparator into to GND.
3. C1 and C2 both ae high-pass filters, which will affect the low-frequency corner of the noise spectrum.
You don't say what type of noise bandwidth you want, and that is important. Do you really want the clock or data input signal frequency to vary from Hz to kHz? Or hundreds of kHz with faster parts? What is it you are trying to achieve?
ak