Yeah that interpretation doesn't make sense as our Lord, Samson, John the baptist and many mediaeval Catholic men had long hair. In nature your hair can get pretty long so I don't see it being unnatural.
It could mean more about a man excessively caring for his hair
I agree with you both, but not sure he would actually scold them for excessive hair care, unless the men were getting perms, color, or curling their hair. I don't know but that seems highly unlikely.
What seems most logical to me is that he was be speaking against the excessive length of men's hair as going against the customs he had previously taught them to adhere to. After all, they did have scissors back then.
But then what about Our Lord and Samson etc.? Were they taught that these were exceptions?
And how exactly would they nourish their hair back then except by washing it?
"14 And whether nature itself does not tell you that long hair on a man is nothing to be admired," - Jerusalem
"14 Doth not even nature itself teach you, that a man indeed, if he nourish his hair, it is a shame unto him?" - DR
"14 Does not nature itself teach you that if a man has long hair, it is a disgrace to him," - Novus Ordo Bible
"14 Does not nature itself teach you that for a man to wear long hair is degrading to him," - random prot bible
"14 Doth not even nature itself teach you, that, if a man have long hair, it is a shame unto him?" - KJV