Don't kid yourself that any cadet scheme is free. It can be dressed up in a few ways, but you are financially disadvantaged in one way or another. I realise that some of these ways are more predictable and stable than others, but it is still money you don't get. Saying it is 'free in the long run' is misleading.
BA have already advertised for FOs with the requirement of an 'EASA issued licence for XX aircraft certification', or words to that effect, so you can apply with an MPL.
As for MPL vs. CPL/IR, other posters are right when they say the view of "ATPL is widely better" isn't accurate. You spend less time in a real aeroplane on an MPL, yes. However, nearly all the time you do spend in a real aeroplane is under 'continuous assessment', i.e. a lot of the time difference is the extra solo that a CPL requires. Solo experience can be great for a lot of things, and I wouldn't sniff at it, but an extra 38 hours is not going to turn you into Neil Armstrong. On an MPL you don't do an IR, or have to do the IR exam, which does seem like cheating a bit. I would say the big disadvantage of not coming out of training with a CPL/IR is that you can't do certain side jobs that some people do, e.g. paradropping.
As people have already alluded to, whether you've done more real flying, or spent 170 hours in a sim, you're still going to be a rabbit in the headlights when you get to a real flight deck. I think the best thing about a mentored scheme of any kind is that it is targetted, so you are getting used to a particular airline's SOPs from day one, which should make the transition to line flying slightly less difficult.