BA specifically advertises First as 'A haven of calm'. As such I strongly believe that BA has a duty to at least try to deliver this. A 'no babies in F' rule and a code of conduct for everyone else in F would be a good start.
Yeah. Good luck with wishing for that. Because that would kill revenue stone dead in a nanosecond. Not because people would be incapable of abiding by it, but because they would deeply resent paying £££/$$$ for a seat and then be told how to behave.
Yiou don't work in marketing, do you?