The Republican era Romans (who campaigned non-stop) shined their armor. During the Mithridates War in the 1st Cent BC, it was reported that part of the Roman prelude to battle was shining armor to a high polished buff; it was one way an enemy actually knew the Romans were serious about fighting a battle.
I don't know why anyone would purposely make their armor look like that picture, its hideous. Simply wiping the iron down nightly to remove moisture and ensuring its always coating with oil would be enough to keep it rust free. Besides, they'd still have to buff all the brass/bronze on the lorica, helmets, and swords, and oil all the leather.
Can't speak to the period use of rust-finishes--Ill leave that to others.
However, I wouldn't call that a patina. That's straight-up active rust that'll continue to corrode the metal.
I've rescued some items (hatchets, axes, non-Roman armor, etc.) from rusty oblivion by wire brushing/steel wooing/sanding with plenty of oil and they developed a smooth, very dark brown or even black coloration.
Definitely NOT rust colored and powdery like those pics. That's not a patina--that's neglect.