This question may be based on a wrong presumption, but it appears like the start of the "Imperial" phase of Rome's history with the Julio-Claudian dynasty sparked a more overt phase of scheming, assassination, and infighting compared to other phases in Rome's history.
Specifically, I am interested in how most or all of the natural heirs or even the favored adopted heirs were killed early, and likely murdered. For example, most of Augustus' heirs were killed, and Agrippa's lineage was wiped out, all in front of his eyes. This didn't seem unique to any particular emperor. Was this scheming/infighting the start of a new form of politics? Or was it already within Rome's political norms?
I think you're working from some misinformation here. What are these assassinations you're talking about during Augustus' and Agrippa's lifetime? What evidence do you have that Marcellus, Gaius, and Lucius died anything but natural deaths, as is pretty much universally believed? Tacitus thinks that Livia killed Agrippa's sons, but there's no evidence of it and his accusations, which fit into his general dislike of Livia and the invective that he surrounds her with, are usually discarded. Moreover, your chronology is wrong. Not only were Lucius and Caesar almost certainly not the victims of murder but they hardly were "wiped out, all in front of [Agrippa's] eyes." Agrippa died more than a decade before either of his sons. The first good evidence we have for any imperial assassination is the public murder of Caligula in 41.