Rationale for operating the diode in the (reverse biased) breakdown region
Three reasons:

First, operating in the forward orientation only allows operation at a single voltage, nominally about 0.7 volts for a silicon diode. Diode construction can be tailored to produce a wide range of breakdown voltages, with a consequent choice of different regulator outputs.

Second, your V-I curve overstates the sharpness of a forward-biased junction. There is no relatively flat portion other than in the vicinity of zero, and that's not very useful.

Third, with an exponential V-I curve, the forward-biased junction cannot be operated at useful current levels with good regulation.