Historians mostly agree that Romulus Augustus was not the last Roman emperor and Julius Nepos was. I’ve always been confused why because Julius Nepos never really had power and just claimed to be the rightful Roman emperor.
It's a bit difficult to tackle this entirely, I've tried to find any books available to me that argues otherwise that Nepos was the last roman emperor in modern historiography. But from what I've read, that seems to be largely not the case at all.
One reason one might see it that way, or interpret it as such, is because the Eastern Roman Empire did however completely ignore the fact that Odavacer was in complete control without the senate support, and merely considered him as a patricius until Nepos came back to Italy to rule.
The Byzantine scholars Procopius of Caesarea and Theophanes the Confessor even wrote much later that Odavacer fulfilled the criteria of ancient roman law. That is, of course, until 480 CE when Nepos was murdered and the eastern roman emperor Zeno was tired of Odavacer incursions into his realm and argued that he disregarded roman law, therefore sending Theoderic to subdue him - Zeno in theory, though not in practice, considered himself the sole ruler of both east and western roman empire.
But it is difficult not to argue that Romulus Augustus (or Augustulus, the little August) was the last western roman empire - as he was the last to be approved by the senate (though not acknowledged by the court of the eastern roman empire). Though some would argue that the removal of Romulus was not as much as the fall of the western roman empire, as it was rather a failed coup. At that time there were four emperor's in the west and east: Romulus and Nepos in the west and Basilicus and Zeno in the east.
Though one argument can be made that since Nepos had ruled in the west before, between june 474 - august 475, and his rule, some would argue, then had more legitimacy than Augustulus. Therefore one could argue he was the last strong (for the lack of better word) emperor of the western empire. But he never thrived well in Rome and his experiences and template being raised in the eastern roman court did nothing but alienate the senate and the situation in Rome - especially after the loss of Zeno's support in the east - would most likely have ended in failure regardless.
Sources:
Hughes, Ian. 2015, Patricians and Emperors : The Last Rulers of the Western Roman Empire
Elvers, Karl-Ludwig (Bochum), Eigler, Ulrich (Zürich), and Leppin, Hartmut (Hannover). ‘Nepos’. Brill’s New Pauly. Ed. Hubert Cancik and et al. Brill Reference Online. Web. 20 May 2020.
Bendlin, Andreas (Erfurt), Leppin, Hartmut (Hannover), Groß-Albenhausen, Kirsten (Frankfurt/Main), Bleckmann, Bruno (Strasbourg), and Küppers, Jochem (Düsseldorf). ‘Romulus’. Brill’s New Pauly. Ed. Hubert Cancik and et al. Brill Reference Online. Web. 20 May 2020.