Is it now?
I would say it is natural for humans to do what children do naturally.
One thing children do naturally is verbalize in "non acceptable" childish ways. For instance they will say "He gone a loooooooooooong time." when they mean he was gone for an extremely long period of time. It is considered cute but children are discouraged from doing this as hearing people make the words do the work, not the tone of voice, expressions, or other vocal trick.
Another is to use their face, hands, body, and movement to express things. Once again this is considered cute when children are young, but this natural tendency is discouraged because in the hearing culture words, not actions, are expected to carry the entire weight of the communication, not "body language."
Having watched a lot of hearing children grow up I would say the precepts ASL is built on is just as natural to humans as the precepts spoken language is built upon.
The difference is speaking people often reject nonverbal communication for lousy reasons making it unnecessarily difficult for deaf people who find verbalizing difficult to begin with.
If ASL precepts are as natural to hearing children as speaking, then how can ASL not be the "natural language" of Deaf Americans?