technically this was what was happening in Otl, first with Theodoric the Great and then subsequently with the Franks ( and even subsequently given that every political entity in Europe had as its highest ambition to be the chief heir of Rome ), but two things prevented this development, the wars of Justinian which caused romanitas ( understood as "ethnicity" ) to decline outside the Empire, because it was considered a dangerous fifth column by the remaining Roman-Germanic states, or I conflict with the idea that was had of it between the capital ( Constantinople ) and the outskirts of the state, and subsequently another thing to consider which, let's say, had a negative influence, the chances of seeing a successor of Rome in the short term were the Salic law ( which has notable similarities with the late imperial tradition of dividing power between several Caesars ) which prevented the Franks from creating a solid and cohesive state to last long enough ( in the sense of avoiding civil wars within it and directing those resources into consolidating its territorial gains more easily in west of Rhineland and in other regions ), so as to allow a process of assimilation of minorities not " romances " within it, on a large scale
It must also be considered that technically there is another factor that perhaps had a negative influence on the continuation of Roman imperial history ( in the West ), namely the impossibility of taking the purple by "ethnic" non-Romans, in particular towards the Germanic people, which if it had happened would probably have favored a greater integration of those populations into the empire, given their small number compared to the Roman populations ( certainly a similar development also occurred in Otl, but it was only partially, just quote Theodoric's phrase the Great : the rich Goth imitates the Roman, while the poor Roman tries to pass for a simple Goth ) furthermore there was the problem caused by the senatorial opposition who did not want to pay to defend territories that were not theirs ( the Italy ) is that they favored the Caesars who agreed with their political visions ( just look at the fate of Anthemius, who, being a patrician from Gaul, rightly wanted to focus on the defense of the entire Rhine limes, something that the Italian senators did not like, who decided that she was not an Emperor to their taste ) so I believe that this detail also influenced the chances of seeing an imperial rebirth in the long term, certainly as I already said in the previous comment, there were subsequent attempts which were very promising ( the ideas of Theodoric the Great, the Franks ( who technically already had the first chance to obtain the imperial purple in the midst of the iconoclastic crisis during the reign of Leo III, while already under the reign of Childebert I, we have the first military campaigns of the Franks in the peninsula ), the Justinian conquests, the possible division of the Empire between the sons of Maurizio and up to the 19th century ( certainly these last attempts would not properly be definable as a Roman state, but rather as its legitimate successor ( be it a centralized HRE, the Capetians obtaining the imperial throne, a Macedonian dynasty that does not collapse, so as to maintain the remaining possessions in Southern Italy ( 1 ), a more successful Habsburg Empire ( I'm talking about all of two dynastic branches, the imperial one and the Spanish one ) , a Plantagenet France, or the France that manages to peacefully annex Burgundy in its entirety in the 15th century, and which then focuses on Italy, or in finally with Napoleonic Europe )
1 ) or a more successful Komnenos revival, or even the Italian expedition of Manuel I which continues to maintain the promising initial results ( yes, I know very well that Byzantium is the ERE, I simply put it together with the other scenarios for simplicity )