Rome took some unexpected Ls against the barbarians too. Didn’t change the trajectory of the empire.
Who were the barbarians, really? Caesar’s conquest of Gaul was basically a massive human trafficking organization that functioned as a pyramid scheme, and Rome only went downhill (in terms of basic human decency) from there.
The "trajectory of the empire" is that it became the Roman Catholic Church. Rome still rules a sizable portion of the world's population.
I wonder if the USA is going the same way. Democratic Church of America?
The failure to integrate the barbarian Goth refugees is generally marked as the beginning of the fall - and absolutely changed the trajectory of the empire.