The falling object doesn't accelerate. You, standing on the ground are the one that's accelerating. You see the object as accelerating but that's an illusion due to frames of reference.
As evidence: which object feels a force on it?
You can feel the force the ground continually pushes up at you. The ground is accelerating you up. The falling object is completely idle in its inertial frame and feels nothing.
Ok so that makes sense, but if we are accelerating by standing on the ground, isn't that implying that we are continuously increasing in energy? Couldn't that be harvested for a perpetual motion machine of some sort?