I would think that would depend more on the limits of Gondor’s bureaucracy and of their communications and recordkeeping technology? I mean, later Roman emperors’ abilities to intervene in the lives of most people were limited, even when they wanted to intervene.
Like, because this is a society that doesn’t have computers and literacy is probably restricted to a minority of the population, I’d expect that Aragorn and Faramir would have their hands full with the doing all the basic government things, and especially rebuilding them after the war.
Yeah this is one instance where my gut says later Rome (and Byzantium) is less of a good match. I'd imagine that Aragornian Gondor was a lot tighter ship than late Rome or Byzantium, and also the threats within & without were less existential.