My point stands. Think about it this way...
You decide to slash your odds by going to FTE and make it through to the final selection day. At the final selection day you meet the best candidates from the other two schools (the same schools you avoided). Now all the best candidates are in one place, competing against each other for the places, and you have to beat them to progress anyway. So under no circumstances are you actually avoiding any of the competition (at least not as far as the FPP as a whole is concerned), assuming BA are choosing candidates based entirely on merit, rather than allocating to each FTO an equal number (which they almost certainly aren't). It's inconceivable that BA would do it that way, given that they want the best - not the luckiest. And in this industry the FTOs don't make the demands - the airlines do.