Double check my inferior intellect please: with a traditional single piston floating caliper, the caliper moves toward the center of the vehicle as the pads wear and the piston travels outward, yes??
As the brake piston pushes the inner brake pad against the proximal rotor surface, the floating caliper slides inward and presses the outer brake pad against the distal surface of the rotor. As the pads wear the brake piston has to travel ever farther and the caliper must move increasingly inward.
I just replaced a caliper assembly of the type you described that was seized (lower pin frozen) and would not float. The piston was still able to push the inner brake pad for braking, as evidenced by the completely worn inner pad. Outer pad looked like new.