IMHO (but I do not have hard evidence apart from maybe my OpUps from J to F) BA F revenue is mostly coming from 2-4-1, OpUps (still good money paid for J ticket), FF redemptions, buy J fly F on one segment promotions (to give them an advantage over Virgin for high yield traffic), staff etc. and not from full fare passengers as there are quite a few of them. So, I guess, BA needs more seats to make this product to make money.
I don't think BA would bother having F if a significant part of that cabin was 'non revenue'.
I know several routes with a healthy amount of paid seats (although maybe a chunk of A rather than F)