That isn’t how Rome fell though it may have been a contributing factor. Military spending was arguably larger in the early days when the empire was expanding. Factors that were a more proximate cause of Rome’s fall were:
- The large influx of barbarian immigrants who were eventually allowed to establish zones in which their law, and not Roman law, held sway.
- The improvement in barbarian military capabilities and their increasing familiarity with Roman weaponry, organization, and tactics. Many barbarian troops had served in or had fought alongside Roman legions and many of their leaders had spent time in Roman imperial courts.
- The rise of a new religion, Christianity, that even after it became the state religion, advanced an ideology that undercut the conceptual foundations of the classical world.
- The ravages of the plague: recurring waves killed a significant fraction of Roman citizens.
- Economic stagnation, ruinous taxation, decline of individual landowners and rise of large landed estates, legal restrictions on vocational mobility, extremes of wealth and poverty.
- Incessant internal struggles and civil wars. Lack of accepted way to resolve problem of succession.
- Decline of the Senate and many institutions of the Republic and Classical society.
Others may disagree with the specifics on this list and suggests various additions and revisions. However no knowledge commentators will reduce it to the single simplistic cause of “how military empires fall and fail".
It is also crucial to realize the Eastern part of the Roman empire did not fall, but lived on a thousand years as the Byzantine empire.
None of this is to suggest the costly interventions in Vietnam, Iraq, and Syria were anything but ill- advised. Trump campaigned on being much more cautious about intervention but appears to have been pushed by opposition political forces into at least a few strikes in Syria and continuing and deepening involvement in Afghanistan.