Have you inspected the front brake system ? You might pull the wheel and insure that the cam has not worn channels in the shoes . Or that the cam has not been worn to flat spots where it contacts the shoes . Or that the lever is not adjusted to tight , which brings the cam too far around and sticks .
You might also insure that the hand lever functions smoothly , as it should .
Any of those situations could easily bluff a man into thinking the cable is the problem . (edited)