Mike Duncan does indeed do a pretty good job of describing the situation. I do think that the idea that the military as a whole expected to be continuously bribed is a bit of an exaggeration, but the problem of donatives and related currency the basement is definitely a noteworthy example of the probles the empire faced during that time. However, I would say they're more of a symptom that a cause.
I just say that simply having a more stable civil administration at this time would avoid much of the issue. For example, one of my favorite POD's is the idea of Alexander Severus not being assassinated. If we can get a few decades out of him, we avoid much of that political and economic instability, we avoid army after army needing donatives.
In the end, I would say that the problems were more economic and political than military. Consider, after all, what got Alexander Severus assassinated in the first place: he negotiated with the enemy rather than fight. Clearly, and army that would rather risk their lives than except a negotiated peace has the necessary martial virtues to maintain an empire. In fact, as you progress through Duncan's podcast, you will see many of these barracks emperors and their legions focus more on defending the empire that actually wedding there civil wars. Maximinus Thrax and Postumus are notable examples. It almost seems that the military was the least rotten component of the Roman government at that time.