Modest dress doesn't satisfy an explicit command to demonstrate man's headship over woman. Modest dress was assumed back then, and Paul wasn't satisfied with it.He mentions head coverings in the context of speaking about "headship" and long hair. He doesn't suggest any other symbol is acceptable, and he requires this practice in all churches -- even where the symbol was the *opposite* of what the culture expected of men and women.
I realize this is a hobbyhorse for people like your. I've discussed the stock objections before. I'm not going to repeat myself.