Simple, it's down to money. It's also nothing to do with any of the pilots except the training department as to who gets accepted and who not.
Financially and statistically it has been proven that low houred (as in ab-initio) modular pilots have more difficulty in passing the type rating than those who have completed an integrated course. The ability to assess a student (SEP entry pilot) based upon concise, coherent written reports is a whole lot more enticing to a bean counter counting the training budget.
It is nothing to do with which is better and which is worse it is all to do with reducing the cost of the training package by picking those students that, in the opinion of the training managers, have a greater chance of passing the course to the required standard first time without repeats if possible. Next time you want to take a look at the cost of a 4 hour sim detail. As to the same quirks between the MOD and Integrated, then the integrated student will, hopefully, have had these 'quirks' reported thus enabling the selection to be done knowing those quirks and not after ward in the sim.
BA do take modular pilots, however they tend to take them as DEP after they have had a few hours in other companies. There are an awful lot of Easyjet and Ryanair pilots in the RHS at the moment who were, previously, modular.
There is no arrogance, holier than thou or malicious attitude. It is purely down to cost, cost and more cost.
Some might say that you have a particular axe to grind on this one?
As to the sponsorship, as Re Heat has constantly replied, it was toyed about last year as an integrated scheme to be run along the lines of the old Prestwick college. With the downturn all ideas have been shelved. When the up turn arrives though the company will, undoubtedly, want to be in a position to 'just add water' and expand to a position where they can take advantage of the up turn. Start looking then! Flight International always carries the BA recruiting adverts.