This thread has to end as it is futile. BA will never ban babies from First period. There are too many influential people that travel with kids let alone it would be seen as discrimination and another PR nightmare for them.
Forget it guys - if a baby cries in F then I promise you the baby will be feeling worse than you and most parents will too.
And my final point - if the parents are acting like they don't care, tackle them on the issue. Don't expect someone else to do it for you or sit there huffing and puffing! You're paying extra cash for a bigger seat, fewer seats and (ahem) better food and booze, not for a public free zone....you need to pay a tad more for privacy