Springs are made of special heat treated steel alloys due to modulus of elasticity and fatigue life. With the right alloy a aluminum spring could be made but it's life would be very short and allowed deflection pretty minimal. Aluminum has about 1/3 the bending stiffness and strength of steel the same diameter. Take a 1/2" aluminum bar and a steel one and the aluminum will bend much easier. Read the frame materials discussion it "Bicycling Science" third edition, published by MIT Press. It is available on Amazon.

Stiff aluminum frames are due to very oversized tubing being used as compared to normal steel tubing used in frames.

In addition to stiffness racers like compact frames due to their lowering the frame center of mass enough so that when out of the saddle the bike feels lighter and more responsive.