I'm a big proponent of careful, regular inspections. But they can't catch everything...I did have a mixture cable seize up at about 300 hrs TTSN. No warning whatsoever in terms of change in stiffness, free play or feel beforehand. It was certainly an anomaly, but threads like this are good to think through the response if the unexpected happens.
It would be interesting to know why it seized up. There were some problems with cables that had nylon liners in them, and if the cable was routed close to the exhaust that nylon could melt and seize the cable.
I've seen a carb heat cable break due to misrigging. The wire wasn't clamped properly by the clamp bolt, which had an extra washer under its head, so that once the wire was secure the bolt wouldn't turn in the lever as the cable moved it back and forth, and the wire fatigued and failed. Another carb heat control failed when its wire got so deeply grooved as it vibrated inside the housing (which is a tightly coiled wire) and it broke at one of the grooves. Takes many hours to do that, more than a TBO. I've found carb heat cable clamp bolts worn three-quarters of the way through, and the hole in the lever nearly worn right through the edge of the lever. A carb heat failure in the right sort of engine on a day when the carb ice risk is high could be fatal.
A throttle cable failed due to old age when the student yanked it back as the airplane went into an intentional spin, and the engine went to idle; the instructor took control and set up for a forced approach, and in the glide he told the student to stick the throttle knob and shaft back in the hole (the wire had broken right at the end of the shaft) and it pushed the wire and the engine went to full power so they flew home. That sort of luck would be rare indeed.
Some carb throttle levers have a spring to take the throttle wide open if the cable fails. I've only seen a few carbs with that, and no injection servos. Never seen a mixture control that's sprung to full rich, either. Cable failures can have serious and expensive consequences.
Flap failures? Fraying or corroded cables. A friend had one flap suddenly retract from 20° to full-up right after takeoff in a 185 floatplane; the airplane rolled and hit the water. The pilot and single passenger got out and swam to shore. Could have been a lot worse. The down-cable on that flap had failed. Those cables run under the floor and up the rear doorposts and are hard to inspect without taking the interior out. It costs money to do that, so it often ain't done. I used to find lots of interesting and scary stuff.