At the same times, the Romans did turn into cowards by the late Roman times. I cannot help but recount when Valentian, (frustrated at the decades of having to deal with potential recruits who cut off their thumbs to avoid military service, despite the laws forbidding very specifically such form of self-mutilation) simply instituted the penalty of death by slow immolation. Then came Theodosius who repealed that, and instead decreed that landowners must supply another recruit for every mutilated one. That stopped it, but the problem did resurface some time later. That is when the Romans turned to the "barbarians" to almost wholly supply their army with soldiers.
Actually no, unless you can provide credible statements. The Late Roman army was still capable of defeating "barbarians", and the majority of late roman soldiers was never of "barbarian", but of roman origin. Roman armies always had a sizeable amount of foreign auxliaries and that time was no exception.

The cause of the decline of the Western Empire was not military but economical. With the money for self-defense decreasing, there was no way troops could be sustained thus, and the majority of "conquests" at the time by "barbarians" was made not by destroying resistances but by simply occupying what was being constantly neglected or undefended. At Chalôns, however, Atilla got it handed to him and the Eastern Roman Army reached its peak under Narses and Belisarius.

Still, just think the desperation of the Romans - to slice off your thumb just to avoid the army... Your opposable appendage, with one that you are enabled to grasp things. Of course, the streaks of defeats, the innumerable hordes of invading nomads and other tribes, the much lower professionalism of the Roman Army, but still... The Romans were indeed decadent and pampered by then.
Myth, of course. Was the re-institution of Decimation by Crassus a sign of decline and cowardice of all Roman armies?