Well, maybe not all the emperors were considered especially good, but it does seem strange that multiple competent emperors were followed by sons who weren't adopted into the family who did such a terrible job.
The examples:
Nero following his father Claudius. I know Nero had 5 good years, but why not more.
Commodus following his father Marcus Aurelius. Marcus seemed pretty good, and had Commodus triumph with him, so why did Commodus attempt to change the name of Rome and attempt to be a gladiator?
Caracalla following Septimius Severus. He killed his own brother to have the empire to himself. Septimius also seemed pretty cool, especially according to Tacitus. So what gives?
Edit: I guess Domitian following Vespasian could also count, though Vespasian had really prepared his other son Titus for the job. I assume the 'heir and a spare' idea wasn't too important for Vespasian.
Nero wasn't Claudius' son. Nero was Claudius' adopted son. I'm also unsure why you should think this to be a lot of emperors--this is a set of three (one of whom isn't the biological son of his father) emperors who were considered bad by some of their contemporaries (though not all--Nero, for example, was beloved by the free cities of Greece, and both Caracalla and Commodus appear to have enjoyed wide support among large segments of the population) out of a collection of several hundred emperors.