It's not wear. It's very specifically at the cable clamp on the brake arm. I've never had a cable break anywhere else. As the brake pads wear I adjust the cable length to maintain a sharp brake action. This undoing and redoing of the clamp on the cable breaks strands over repeats. It's certainly safe to carry on riding when 1 strand fails.... this is the first time I've noticed multiple failures.
This is on a commuting bike ridden every day. Having out of action every couple of months because a strand has broken costs quite a bit more.
And no I'm not expecting a definitive answer, I'm just surprised people are replacing it immediately.
Why would it be out of action? Replacing the cable takes only a few seconds longer than the reclamping you're doing.
Also, I'm not sure why you're having to reclamp; all the brakes I've ever had have sufficient tension adjustment to allow for pad wear. You should just be able to turn the screw a bit.
And cables fraying every couple of months? How often are you reclamping them? IME brake cables last pretty much forever. Gear cables fail much more often.
But yes, there's absolutely no way I'd ever knowingly ride a bike with even one broken strand. Keep a spare cable, replace immediately.