The problem is that we seem to think we know what the Romans made their Pteruges out of. But as far as I know, Greek (and by extrapolation Macedonian and by further extrapolation Carthaginian) Linothorax is still not definitively nailed down as a thing, so what Pteryges were made of we cannot say There are still advocates of the ‘padded linen’ school of thought, though having played around with gluing multiple layers of denim together myself* I am sure it would have made an excellent form of armour, as long as you didn’t get it wet. or sweat.
The only actual ‘Linothorax’ we have is the one from the Vergina tomb, and that was made of Iron, so not much help.
Myself, my Macedonians and Carthaginians have Linen dangly-bits. It looks nice.
*which may seem cockamamy but I have seen more half-assed ‘Experimental Archaeology’ given respect. One of Britain’s most eminent old-timey archaeologists ‘settled’ an argument he was having about the efficacy of the Sling by making one, walking out into a field, and using it by twirling it round his head and letting go. His conclusion that slings were not much cop was published without any adverse comment I heard of.