To avoid angering Medievalists, I'm going to define the warfare you are thinking of as "in which one subpolitical entity goes to war with another pursuing aims specific to the subpolitical entity, rather than broader national ones". For example, if Governor Roy Cooper of North Carolina marched on Charleston to declare South Carolina dissolved and incorporated into a Greater Carolinian Republic, this would "feudal warfare" as you are thinking of it. This can be in opposition to if Governor Cooper marched on Washington DC to declare himself President of the United States.

In short, the former only happened in very particular times and never with the aims of redrawing administrative boundaries, while the latter was more common (although not as common as is often said). In general, feudal warfare requires a very specific and specifically local orientation of politics, in that the military power and leadership of a region need to identify themselves with that region in particular--to continue the hypothetical, Governor Cooper would need to see the annexation of South Carolina as beneficial and people would need to go along with it. There also needs to be a significant decentralized, local component to administration--Cooper would need it as plausible that this annexation would stick.

These conditions did not exist in the Roman empire, or at least did not usually. The governors of the provincial administration and a significant portion of their subordinates were centrally appointed and sent out to the provinces from the imperial center at Rome. They were not necessarily from Rome--although many were--but Rome is where they derived their power, as opposed to deriving it from local ties. Likewise, administrative reorganizations, even if they were undertaken through the initiative of a governor, were done centrally. Perhaps most important was the social psychology of it all--the idea of the governor of Cappadocia invading Bithynia to increase the provincial boundaries would be absurd. For one, it wouldn't stick, but more importantly, this was a temporary post that lasted ten years at the longest. The political goal of a governor was not to increase the power of their administrative post, but rather to increase their own standing within the political world of the Roman center. Provincial power was a tool, not an end.

There is also the matter of the soldiers. They did have a certain regional identity--the German legions, for example, often acted as a political bloc, as did the British legions and the Asian legions. But this did not mean they identified themselves with the territory they were stationed in. It is hard to tell specifically, and probably varied by region (my information comes from North Africa, specifically Cherry's Frontier and Society in Roman North Africa which looks largely at marriage patterns) but the military tended to be somewhat socially isolated from the nearby non-colonial civilian populations. Furthermore, after Batavian Revolt in 69 CE it became policy too station soldiers far from their homelands--one of the classic examples is Flavius Cerialis and the Batavian cohort he commanded at Vindolanda fort along Hadrian's Wall. So not only would the leaders have no particular desire to engage in "feudal warfare", but neither would the soldiers.

What I am saying is not universally true, of course. During the Third Century Crisis, for example, the empire effectively split into three parts, the central provinces commanded from Rome, the northwest provinces commanded from Cologne, and the eastern provinces commanded from Palmyra. These three did engage in conflict that looks a bit feudal, even if it only lasted a couple decades. On a smaller scale, during this time the "bagaudae" appeared, a rather enigmatic term for combatants in Gaul or Spain. We don't really know who these were, and explanations have veered from peasant rebels to anti-imperialist insurgents to opportunistic bandits to local self defense forces to proto-feudal militia commanded by local powers. These might be an example, but again they are situated within a very specific context. Much later, the actual breakup of the empire in the west was a combination of Romano-Germanic armies conquering new territories and those territories breaking off of the imperial center. And finally, there were particular regions within the empire that resisted central control and engaged in periodic warfare with neighbors, but these were very unusual spaces.

So in short, Roman armies might fight on behalf of the Roman empire as a whole, but only very rarely on behalf of their particular province.

As always, I would recommend Greg Woolf's Roman: An Empire's Story as being perhaps the best single volume history of the Roman empire.