Why do we have to check the speed brakes during GPWS memory items on an A320?
Because that is how American Airlines Flight 965 went down.

Long story short, the pilots deployed the speed brakes to increase descent rate during approach, and did not notice they were off course. The GPWS warning sounded. The pilots reacted within one second. They did everything they could - except they did not retract the speed brakes. They crashed.

Why is it a memory item? Because GPWS means imminent terrain contact. You don't want to wait around for some automatic mechanism to retract the speed brakes for you. Let alone take the chance of that mechanism failed. You do it. NOW.