I am not sure this is a universal rule. Many emperors had houses full of children, some of them ruling one after another (vide Vespasian's sons, Titus and Domitian). read more
Yet, Caesar, Octavian and Tiberius did have legitimate children of their own, only the fates so decided that the first two only had daughters that reached maturity during their reign, and Tiberius’ direct male heir died before his father. read more
Only about 30 Roman Emperors ever reigned for longer than 10 years. That simply just doesn't leave a ton of time to have a family, especially when lots of the men who would become Emperor spent a long portion of their lives playing military and political games in order to acquire their position of power, rather than marrying and producing offspring. read more
So while all three emperors did marry and produce biological children, and both Caligula and Nero died much too early to have produced adult blood-heirs, I believe that their failure to create or maintain political stability and their failure to have an heir "ready to go" in case of early demise demonstrates less focus on dynastic stability than Julius, Augustus, or Claudius. read more