I would expect a forward biased regular diode to be used. Especially in applications in which you don't expect a change in current direction. Is the curve more predictable in the reverse biased state?
The curve is much more useful in the reverse breakdown mode. Especially for avalanche diodes, which every "Zener" diode over above 5V actually is.
Here I have swept the current from 100uA to 100mA on each type of "regulator" diode.
Compare the regulation of each:
Temperature coefficient is also ~4x better, about +6.5mV/°C vs. roughly -25mV/°C
A forward-biased silicon diode (zener or "normal") will have a voltage drop of about 0.7 volts - not too useful for voltage regulation.
Zener diodes can be made with many diffrerent reverse breakdown voltages, so you can use them in suitable circuits to produce many different regulated voltages.