Unlike FAR 23, there are no requirements for cable specifications on LSA aircrafts, so they there is no warranty they are really so strong as you said.Primary control surfaces require 1/8" minimum, 7 x 19 galvanized cable. It has a breaking strength of 2000 pounds and a rated working load of 400 pounds. When fittings are attached, it is tested to 60 percent of breaking strength, 1200 pounds, for a minimum of three minutes, far beyond what it will experience in the airplane. 1200 pounds on the cable once installed would crush pulleys and buckle their brackets and and tear out control surface bellcranks and probably do extensive damage to the rest of the airframe structure.
LATER EDIT: I can't recall any other mechanical failure which can lead to inflight breakup, of course, excepting itself structural failure and I won't make it an issue, there are a lot of founded reasons for that: they are strong enough structurally, there are specific strength standards regarding this issue, also, I can't recall any structural failure crashes where the causal factors were others than pushing the envelope, initial type flight tests, poorly structural designed types with obvious and numerous crashes due to that, or very high carelessness maintenance. Unfortunately, can't say the same for cable failures... if it would be so, I would not wonder about it.Worrying about properly designed systems and their cables will lead to worrying about every other little thing in the airplane and you will never fly it.
And even if there are any structural failures, they are very isolated cases. The airframe structure undergoes more thorough inspections to detect early any structural failure and generally it's given much more attention to structural fatigue and other problems and that makes the structure less prone to failure, because any problem it is earlier detected. It's normal and obvious that the structure is more closely analyzed than cables to detect these problems.
LATER EDIT: And maybe that's all we can do from a practical standpoint to detect fatigue and other structural failure issues, it can't be 100% virtually safe, but regarding this thread issue, if not mass-balanced surfaces choice would be likely to flutter, it seems it's just unnecessary risk taking for an issue with catastrophic consequences. You got my point?