The use of "Roman Arms Factories" was not restricted to the Late Roman period. During the second Punic War, Rome fought the Barcids in Spain, a long way from the arms workshops of Italy, with concurrent long supply lines, even by sea.
Scipio's master stroke was to seize the capital and supply base of the Barcids in Spain, Cartago(Cartagena) in 210 Bc after one of History's most famous forced marches ( see the 'Legionary feats of fitness thread'). With it came 120 catapults/Stone throwers of the largest sort, 281 smaller ones; 23 large,52 smaller balllistae; countless scorpions large and small; missiles and weapons of all sorts. There was also a considerable amount of treasure, and grain by the silo, 63 merchant vessels with their cargo......
More importantly, all the Spanish tribal Hostages to Carthage fell into his hands...... AND....
the vast Barcid Arsenal where weapons of all sorts were made, especially shields. The size of this can be gauged from the fact that the number of artisans came to 2,000 ( though not all of these may have worked in the arms industry), who as captives became public slaves of Rome, but to whom Scipio promised freedom at the end of the war, provided they worked well.......
(Polyb. X.17 ; Livy XXVI.48 )
Clearly, large Arsenals/factories had a history going back well before Late Roman times....