As a parent and a frequent flyer, who will soon be taking mini MAN Pax (20 mths) to BGI in 1st, I can see both sides of the case.
I think that BA and VS could both accommodate the serious no children element by making the upper deck of the 747 either a child permitted or no child zone, depending on the demand for either. On main business routes where people are paying a premium price to arrive rested and ready to work the following day, I believe that there should be some protection of that right. On mainly leisure routes, BGI, MRU, etc., I think you have to be a little more flexible.
But, this is no way excuses poor behaviour from Parents, Children or Spoilt Children masquerading as 45 year old Pax!