On the A320 why do we follow this particular sequence of taking flaps and gear?
You would want to start with flaps/slats. The landing gear slows the aircraft down like an airbrake, and you'll need a higher lift coefficient to retain enough lift. Slats are a safety feature that allow for a higher angle of attack for the main wing, flaps provide a higher $C_L$ by themselves. So you start with a higher $C_L$ and the safety of the slats, then deploy the gear which slows you down, then delay more flap/slat at the lower velocity.

Deploying full flap/slat first and then deploying gear is also not a good idea: speed will be slow already at max flaps, gear deployment brings a significant further deceleration which may have an impact on safety, definitely on continuity throughout the landing process. You are in a queue with lots of others at a busy airport, and want to keep the array of craft flowing without sudden decelerations.