It would be sillier to pay tens of thousands of pounds/dollars/euros for the same licenses
Cambridge university will offer you the same law degree as Bolton university but which one do you think is more likely to get you a job. Also these integrated courses will give you more than just the bare licenses, the likes of oaa and ctc give you an extended MCC with a JOC and advanced jet handling and they will send you to either New Zealand or Arizona which is perfect as your paying for a gap year but doing pilot training at the same time!
arguably better training
There is not point in arguing about that, the instructors at the likes of ctc or oaa have many years experience flying as captains for major airlines however, instructors at modular school will be teenagers with less than 500 hours (they are instructing because they went modular and now can't find airline placement)!
what makes you think they are going to take untagged integrated students?
They are far more likely to take integrated than modular students because they like the 'airline package' that the FTO can provide. The airlines also like the fact the ctc, oaa... are extremely specialised in what they deliver (training pilots for the airlines!). This specialised airline training does not exist in modular schools and, as I said, most modular instructors don't have airline experience.