BA has struggled to find modular people who fit their mould. This is not to say that they lack skills, but there is something of a culture at BA into which people have to fit to ensure the operation works smoothly. They are at liberty to pick and choose, since they offer some of the better terms in the industry, and as such are entitled to hold their views. It is not the be all and end all of a flying career.
Furthermore, BA take people who are mature and of low risk. They tend to have an aversion to people who literally bet it all on a training course and have absolutely no backup plans or career.
Having said that, there are also many exceptions, and indeed modular chaps with low hours who succeeded in BA in the past, and will indeed do so in the future.
BA have severely cut capacity. 2 Jumbos parked at Cardiff, all 757s sold to a third party, along with a 25% reduction in s/h Gatwick flying - this necessitates no further cadet recruitment.
However, they were on the verge of launching a new cadet training programme last year (reputed to be along MPL lines), but in light of the dire economic climate have placed that on hold indefinitely. New recruits over the past 5 years have been integrated only (CTC being the exception as it was not until recently an approved integrated course, but instead had the facets of an integrated course - continuity of training etc).
BA have never charged for TRs.
BA do operate as a commercial operation, and will happily take your cash to teach on a self-funded TR, or indeed charge for other operators. Never for their own new employees.