Thank you for your replies. Here are even more observations and questions for thought!
Reconstruction artwork in a tourist guide shows one of Pompeii's gates in the background with an iron grille in the lunette and rectangular door leaves below.
About shape, presumably, if a gateway is beneath a barrel vault, then rounded door leaves would have to open outward, since they could not fully open inward. From a defender's perspective, would outer doors that opened outward or inward have been better? If outward, then besiegers might more easily have blocked a sortie's egress.
Did Roman gateways even incorporate barrel vaults? The Airfix fort doesn't.
And look at these posh, rectangular Ancient Roman doors:
https://en.wikipedia.org/wiki/File:Bronze_door,_Basilica_di_San_Giovanni,_2013.jpgCould curved door leaves have been reinforced as strongly as rectangular leaves?