The scenario that Romanian arrived from across the Danube does not require that the Romanian Carpathians were completely depopulated. Rather, it is possible that the region’s inhabitants first switched to Slavic – this is supported by a great deal of toponymic evidence – and then later both language shift and the arrival of other populations resulted in the extinction of the Transylvanian and Oltenian dialects of Common Slavonic in favor of Romanian and Hungarian instead.
Then, the contemporary view of the relationship between Romanian and Aromanian is not that they were mere sister dialects of Latin but split up at a much later date – they are too similar for an early split, and it appears that their first layer of Slavic loans is identical, so that means a split after the 6th century CE. The scenario that Romanian nationalists support requires believing that Aromanian results from Romanian speakers from Dacia migrating well to the southwest. That both Romanian and Aromanian came from the Central Balkans instead is viewed as vastly more likely, especially in the light of the advances in the reconstruction of early Albanian (because an array of evidence puts early Albanian in the Central Balkans, not Dacia).
> so after the Roman Empire abandoned Dacia and there no longer was any central administration, the locals were left to themselves
While I know that the story of their ancestors “left to themselves” after Rome withdrew from Dacia persists in Romanian pop culture, it never fit well with the facts. Romanian words like biserica ‘church’ suggest that Romanian’s Latin ancestor remained in contact with the rest of the Mediterranean world for a long time, because only after Constantine in the 4th century were basilica buildings used as Christian churches. Again, this would be easily explainable by an origin in the Central Balkans where those cultural contacts persisted.