According to the answer in this post Taxiing with one engine: Is engine #1 always used or do they switch? Engine #1 is used because it pressurizes the green HYD system which powers the Nose Wheel Steering. I found that, in latest model of A320 and A321, NWS is driven by yellow HYD system that is pressurised by engine #2. However, pilots still use only engine #1 if they want to taxi with one engine running. Is there other reason for using engine #1?
According to the "Supplementary Procedures / Green Operating Procedures - One Engine Taxi" in section PRO-SUP-93-20 of the A320 FCOM:
Use Engine 1 for taxiing because it pressurizes the green hydraulic system (normal braking).
Y ELEC PUMP.............................ON
This pressurizes the yellow hydraulic system (nosewheel steering) without using the PTU.