This is somewhat of a misnomer that is usually popularized by liberal arts programs. It was only because of Rome's complete control and dominance that resources derived from tribute & taxes were able to be directed towards engineering and arts, primarily infrastructure, architecture and literature.
Secondly, Gibbon estimated that slaves represented approximately 50% of the total population of 120m under Roman control. With no possible means of escape, and certain torture and death for non-compliance, Rome was able to utilize this labor pool to manage all forms of food/raw materials/weapons production and build out/maintain vast infrastructure projects.
The reason for Rome's complete (military) control was their development & deployment of advanced (iron) weapons systems. Rome eventually failed because they lost their technological edge in maintaining this military superiority. As the Goths, Vandals and tribes from other outlying regions eventually acquired similar technology, the odds were evened. Combined with more disciplined tactics and renewed vigor, the tribes overwhelmed the depleted Roman legions.
So, why the collapse in commerce, trade and arts during the middle ages? Simple: level playing field. Everyone had access to the same military technology and state of art weapons. This had a two-fold effect: no one had a monopoly on revenue extraction, and all free capital available for investment was poured into military technology.
So, while the arts and commerce suffered, military defense systems aka castles increased in tremendous complexity and engineering capabilities. Two, metallurgy continued to develop apace, resulting in extremely complicated & refined personal armor. Third, and perhaps most importantly, even with all available resources devoted to military funding, it would still take 1000 years before the next great leap in military weaponry was developed: firearms.
As we know, it wasn't until the development of firearms that nation-states began to finally form and (once again) exert territorial control. Only after firm regional boundaries like Britain, France & Germany (HRE) emerged, do we see the return of available funding to arts & the protection of commerce (highway safety). It's not a coincidence that the Renaissance began only around 100 years after effective firearms allowed technology leaders to control regional economies. That is, surplus wealth was finally once again available to divert from military programs.
Rome had a monopoly and lost it. We look to the areas they influenced and see this great body of work, but in general, monopolies always produce stagnation. Competition is what creates innovation. Technology - military and building - is what advanced at a tremendous pace after the fall of the Western empire.