The Roman upper class didn't 'sympathize' with the Goths and other barbs nor were they 'let into the empire' on humanitarian grounds, they forced their way in and inflicted military disasters like Adrianople on the Empire because the Romans were the ones who kept trying to fuck them over (in Adrianople's case they treacherously besieged the Goths, forced them to sell their own children into slavery for rations, and finally tried to murder the Gothic leadership at peace talks; in the case of the 410 sack of Rome they exterminated the families of their own Gothic auxiliaries, driving them to Alaric I's side, then repeatedly tried to murder Alaric at peace negotiations, and so on). The Praetorians already didn't exist by the time of the great Gothic wars (destroyed by Christian emperor Constantine I) and the Senate was fast approaching irrelevance, etc.
Oh, and it was the Christian Eastern Romans who were the ones who finally did what pagan Rome never could and destroy the Ostrogoths, in the process retaking Italy from their clutches. Add that to the scoreboard of Christendom's victories over paganism.