Is that in fact true that it was particularly rare? I mean that more as a rhetorical question than a real one, and as a means of giving me a reason to describe the Julio-Claudian succession, which is quite clearly through the male line. Of the Julio-Claudians Augustus had no natural male issue, and his daughter's sons Gaius and Lucius Caesar died young, and Agrippa Postumus was exiled and therefore stricken from Augustus' will. Inheritance then necessarily passed to Tiberius, who was the closest male relative to Augustus, being his stepson. Tiberius' own son, Drusus, died before Tiberius, and Drusus' son Gemellus was made co-heir in Tiberius' will with Caligula, son of Germanicus, himself the son of Tiberius' brother Drusus. Gemellus died not long after Tiberius, making Caligula the sole inheritor. Caligula had no surviving issue, nor were there really any particularly close relations to be had: as a result the praetorians hailed Claudius emperor, Caligula's uncle and Germanicus' younger brother. Whatever Claudius' disability was it apparently did not prevent him from siring offspring, and he had one son by his first wife (died young), a daughter by his second, and a daughter and a son by his third. The son, Britannicus, died young, and with no surviving male issue Claudius' inheritance passed to Nero, son of his fourth wife Agrippina, who married his second daughter Claudia Octavia. Nero of course only had one child, a daughter who died as an infant, and his death marked the clear end of all branches of the Julio-Claudian line. But as we can see, the bizarre line of succession among the Julio-Claudians was not the result of wanting to avoid inheritance to male offspring. Indeed, whenever possible surviving male offspring were made heirs, and when they died their sons were made heirs. Inheritance passed clearly through the male line, the problem is simply that the male line was troubled by a large number of daughters and early deaths, or at least deaths earlier than the reigning emperor.

The Year of Four Emperors is a non-issue here, but with the Flavians succession was straightforward. Vespasian was lucky enough to have both of his sons outlast him, and his elder, Titus, assumed the imperial inheritance. Titus died young, however, and only left a daughter, whom Domitian declined to marry. This Julia Flavia had no issue at the time of Titus' death, so the inheritance naturally passed to the next male successor, Domitian. Domitian had no surviving male offspring at the time of his death, causing the immediate end to the Flavian line. Nerva is an oddity, being hailed emperor by the senate, but only under the Antonines is adoption from outside the family--not at all a strange practice to the Roman mind--a usual means of establishing inheritance. Nerva left no offspring, and adopted Trajan, who also left no offspring and adopted Hadrian, who also left no offspring but adopted Lucius Aelius and Antoninus Pius as his co-heirs. These two did have offspring, but Lucius Verus died young, though his son Lucius Verus would become Antoninus Pius' co-heir with Marcus Aurelius. Antoninus Pius himself had a daughter to whom he married Marcus Aurelius--the line therefore continued down the male lines (as much as possible) of both co-heirs. All Lucius Verus' offspring died young, and Marcus Aurelius' eldest surviving son Commodus became emperor. After Commodus there was some dynastic wrangling, but the Severans emerged victorious, and with them the clear inheritance through the male line continues, at least briefly. Septimius Severus had two sons, Caracalla and Geta, whom he made his co-heirs. Caracalla had Geta killed but himself left no male issue. Following Caracalla's death there was some weirdness with the praetorian prefect, but eventually Elagabalus, a distant relative by marriage to Caracalla, was installed as the last remaining Severan. So again, where possible the male line was followed. The Flavians had pretty decent luck with not having sons die before them (although there were only three Flavian emperors after all), and the Antonines mostly didn't have any children. But the male line, when extant, was respected. Indeed, inheritance through the male line was much rarer starting in the third century, when the various "barracks emperors" and repeated imperial coups and civil wars completely destabilized the Roman world. The poor luck of previous emperors who either had no male offspring or outlived their sons should not overwhelm the fact that nevertheless the male line was respected, and the adoption of male offspring from succeeding generations when there was no closer relative was standard practice already by the middle Republic at least.