The problem for the Romans was not that they thought they couldn't win in a pitched fight. It was that they calculated that they could not afford the losses a series of pitched battles would incur. So for Stilicho, destroying Alaric would not only cause him to lose too many men that he couldn't replace, but he would lose Alaric's Goths as potential forces at his disposal. The same went for Stilicho's calculations against Radagaisus's forces, for Constantius with the Goths in Spain and southern Gaul. The Roman Empire in the west and east simply could not replace their losses effectively anymore.
Possibly. The question then becomes about why the Germanic peoples had so much more structural robustness and manpower given the relative territories controlled and infrastructure levels.