This is a very interesting question, one that I actually discussed in my MA thesis, but I digress. So to start while your questions are common ones, there are a few flaws I’d like to point out. Namely, the idea that the late Roman Army was composed mostly of “barbarian” troops, this is not true. Yes the Empire did have some recruitment problems during the third century which likely led to a rather significant decrease in the amount of soldiers who were Roman citizens, but Diocletian fixed this by reintroducing conscription (though the practice was never completely thrown out but it was uncommon before this). In fact, while there were a large number of non-Romans in the military by the 4th and 5th centuries, its estimated that they were really only 25% of the Empire’s total manpower. This means that the vast majority of Roman soldiers were still Roman citizens. I will discuss this in more depth in my answer, however. The other thing that I’ll try to answer in more detail in my actual answer to this question, but still want to touch on here, is the idea that these non-Roman soldiers were of “suspect loyalty”. Of course some of these men probably had very little loyalty to the Roman Empire, I mean no group of people ever holds the same beliefs across the board, at the end of the day people are still individuals. But for the most part these were men who volunteered to serve in the military, in fact most non-Romans were willing recruits during this period. They were people who viewed the military as a way to gain access to a better life than what they already had (this can also be said about the groups who migrated into the Empire during this period). These people certainly did not want to overthrow the Roman Empire, they wanted to live within it, and often they wanted the greater protection and stability that it offered. Those things having been said, now its time to get into the real meat of this question.

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So why were there so many non-Roman soldiers in the late Roman army? Well, that answer is complicated, in fact there’s not really one true answer but let’s discuss. To start, there were the recruitment issues that plagued the military throughout the third century. One of the reasons for this problem was Caracalla’s Constitutio Antoniniana which gave Roman citizenship to every free man in the Empire. This was likely done for tax purposes (I only have a basic knowledge of this period so please someone correct me or add to this if need be), but it also meant that the military had lost one of its main incentives, citizenship. Before the easiest way to gain Roman citizenship for those born without it was to serve in the military for whatever the required amount of time was at the time you volunteered. But after Caracalla granted citizenship to a large portion of the Empire’s population this was no longer served as an incentive because they already had citizenship. Other incentives of course would have included steady pay, perhaps adventure for anyone looking for something new, a steady source of food for the hungry and things of that sort, but unless your poor then most of these things would not have appealed to you. I mean why risk your life as a soldier if you already have a comfortable life that you can now make even better because you gained citizenship from the Constitutio Antoniniana? Even for those new citizens who were poor, gaining citizenship was still probably the biggest incentive to serve, because being a Roman citizen gave you more opportunities to better your life.

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Another problem is that the military did not pay as well as it had in the past, so while it was still a source of income, it was not necessarily a great one. Especially not if it meant risking your life. Unfortunately I don’t have extensive knowledge of Rome’s economy so hopefully somebody else can discuss this point further, because it is absolutely an important one.

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Another reason that the Romans started to recruit more foreigners into the military, and even allowed them to serve in regular units as well, is because of the idea that barbarians were all ferocious warriors. This idea was well established in the Empire by the 3rd century, even if it was somewhat of a hyperbole. These peoples probably gained this reputation because of the disorganized manner in which they usually fought. The Romans of course fought in tight formations and were well disciplined, but this was not the case, or at least not always the case, with non-Romans. But that’s not my area of expertise so I’ll leave the more in depth analysis to someone else. What I will discuss, however, is how this influenced the Romans’ recruitment practices. Emperor Gallienus, for instance, established a mobile cavalry force in the mid-3rd century, and most of his men came from the regions of Dalmatia, Pannonia, and Moesia, because these people’s had a reputation for being excellent horsemen, and for being good cavalry soldiers. Zosimus, when writing about Aurelian’s victory over Palmyra specifically mentions the cavalrymen that came from these regions: “Finding the Palmyrene army drawn up before Emisa…he opposed to them the Dalmatian cavalry, the Moesians and Pannonians.” Aurelian’s reign began only two years after the death of Gallienus, so its possible that at least some of these men were the same who had served under Gallienus. But given the fact that Gallienus established his mobile cavalry sometime around 255 Aurelian almost certainly would have needed to replace any of the men who either died, were discharged for various reasons, or had met their service requirements. Since Zosimus explicitly mentions Dalmatians, Moesians, and Pannonians, then we can conclude that either Aurelian continued the practice of recruiting from these regions (which is likely since this was not a new practice by any means), or that these peoples had gained such a reputation during the reign of Gallienus that Aurelian’s cavalry named their units after the regions they came from in order to emulate them. In this case the straightforward answer that they were simply men originally recruited in this region is the most likely to be true and goes to show that once a region became well-known for producing excellent horsemen the Empire would continue to recruit cavalry from amongst the local populations. During the reign of Gallienus its entirely possible that these men were already Roman citizens since the Edict of Caracalla had been issued less than fifty years before he formed the mobile cavalry force, but not necessarily since some of them could have been exempt from the edict or even moved into the region after the fact.