The " One Bad Emperor" Theory of Change: The timelines where you remove an emperor like Nero or Commodus or whatever emperor you personally blame for a lot of Rome's troubles, and Rome is in a significantly better position. Particularly popular to halt the Third Century Crisis, the favorite emperor for these What Ifs is always Commodus, who create a convenient break between the last "good" emperor Marcus Aurelius and the start of all Rome's troubles heading into the Third Century. Ignoring that Commodus's "Level of Badness" for lack of a better term is often over exaggerated (he kept in place many of Marucs Aurelius's own men and his foreign policy was pretty sound, at least early on), it ignores or downplays the many structural factors that were causing the crisis-namely climate change, plague, increased and more intense threats along all of Rome's frontiers, monetary supply issues and all the imperial management issues this in turn created.
Relevant to your One Bad Emperor Goes, Everything is Fine - I'm going to say that there's obviously a lot of the opposite. One Good Emperor would need a lot going his way to respond to some of the empire's really dark periods, not just "personally being both virtuous and able".
The thing with Emperors during the earlier period is that his relationship with the Senate, who he uses to govern the empire and command armies as legates, is very personal. If they cannot trust him to advance their careers and all that goes with it in a safe and orderly manner it causes instability. The very fact of instability leans itself to a nervous central government that hands out more and larger donatives to the troops that often requires the coinage to be debased while at the same pulling troops away from the frontiers so that if the local governor revolts he doesn't have too many veteran soldiers. Which is what weakens the Roman position on the frontier more then the idea that the tribes on the other side are suddenly allot stronger.Agreed-one look at the third century alone and you see the corpses of a lot of "virtuous and able" emperors who were powerless to do more than hastily plug a hole and then die. Diocletian is a notable exception here (though even he had notable failures, from the collapse of the tetrarchy to the his fialed attempts at curbing inflation and the failed persecutions), but even the "successful" emperors of the period like Septimius Severus largely failed to actually significantly alter whatever trajectory the empire was on at the time.
If one removes an bad emperor with one that has a better relationship with the ruling class allot of stability issues will solve itself. One major problem why it ever did after Commudos death was due to the fact their is a civil war in every life time till the end of the Empire.
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