Wheels that fail have usually two things in common:
- The spoke tension is uneven
- The spoke tension is low
Both are signs of poorly built wheels. In theory, you could have a wheel where:
- The spoke tension is even
- The spoke tension is low
...but you almost never see such wheels, because even spoke tension is a sign of a wheel built by a master wheelbuilder, and those master wheelbuilders tighten the spokes all the way to the recommended tension. (I have had such a wheel once, it was the first wheel I built and I didn't have a tensiometer back then so spoke tension was perfectly even but unfortunately too low.)
You can catch uneven spoke tension by plucking the spokes. If you find a spoke that doesn't ping at all but is completely loose, the wheel is already about at most 100 km away from destruction. If the "ping" sounds is of the same pitch on all spokes, the wheel is good, but if you can hear variation of pitch the wheel is bad.
If you ever find a wheel with low but even spoke tension, you may not be able to diagnose it by plucking the spokes unless you have a reference wheel with identical spoke lengths and thicknesses where the spokes are tightened to the proper tension. But you can immediately diagnose the health of such a wheel by using a tensiometer and finding that the spoke tensions are too low. So yes, tensiometers can diagnose more things than an untrained ear can when plucking the spokes.
Generally the main failure mode of concern is total and complete loss of tensions in all spokes (may happen if tension in sufficiently many spokes is too low), or spokes snapping (happens for poorly built wheels that have not been stress relieved or spoke tensions are uneven or maybe even too low).
The only form of out of trueness that may grow without a total and complete loss of tension in all spokes being a realistic danger is that the spokes have residual twist. That goes away in short time, you hear pinging from the spokes when riding the bike, but if the spokes are sufficiently tight, the out of trueness doesn't grow unbounded but rather results in some residual out of trueness after the residual twist is gone. Most likely you won't even notice it, you just notice the pinging sounds from the spokes. This may annoy you if you run high mechanical advantage rim brakes with very minor pad gap, but may not annoy you if you run disc brakes. However, in 99% of cases if the spokes ping and residual twist goes away, it is a sign that the wheel is poorly built, which means the spoke tensions are most likely both uneven and low, so the wheel is prone to failure in that case too: the failure mode is total and complete loss of tension in all spokes.
Properly built wheels need no truing, ever. You build the wheel once, to high and even spoke tension, and it never needs any adjustment anymore. Learn yourself how to build high quality wheels if you find your wheels need continuous adjusting of spoke tensions. You may start by reading The Bicycle Wheel by Jobst Brandt.