Barbarization?

[CaesarAugustus]

Quite possibly, yes. Although I think it more likely that the defense of the Rhine frontier had been consigned some time before that to settled Frankish and Alamannic groups, as Drinkwater suggests, and the remaining Roman troops pulled back to fortified cities in the hinterland of the limes. A similar sort of thing seems to have been happening on the Danube since the 370s, with the riverine forts and cities being abandoned or turned over to Gothic or other barbarian groups, and 'interior' cities being fortified and garrisoned instead.

So Stilicho may have withdrawn the garrison troops from northern Gallic cities, together with the field army and anything that remained of the troops on the Rhine frontier itself. Those troops that remained in Gaul after that perhaps stayed in their fortified garrisons during the invasion of 406, as the Italian field army troops appear to have done in 408-10.

Later, according to Orosius, what remained of the Roman army in Gaul was sent into Spain by Constantine III, from where it was apparently moved to Africa and then back to Italy.

Honestly I don't think that the defense of the frontier had been consigned. Claudian could have done some embellishing, but he is clear that the border was previously guarded by Roman troops. It is possible that several fortresses were guarded by auxiliary troops, but this was not a novelty. 
For the Danube, it is quite clear that until the defeat of Adrianoplis, the main defense line was organized around roman troops. After Adrianopolis... well, there was the chaos.

For the troops that remained in the fortified garrison... if this is what happened, there is only an explanation: they were few, really few. How is it possible that up to few years before they were able to guard the Rhine, and from one day to another they were neither able to exit from some fortified places, without trying to engage battle? Or even trying to operate logistic warfare?
Simply, this cannot be explained. Unless we read Claudian that replies to our questions. The troops were removed. Sent to Italy? Italy would have been full of men, and it wasn't. So, the idea that some troops were dismissed can not be excluded. And it is also possible that the renewal of the roman troops has been slowed down, further weakening the Roman troops to the advantage of the recruitment of barbaric contingents.