Personally I think its because of history more than anything else. And old boy networks.
Years ago the whole of training department were full of integrated graduates. The Chief pilot was either exRAF or Integrated. His exRAF mate used to work at Hamble now works at Oxford. They are from the same background and trust the others opinion. Life is easy if they keep the status quo.
Now the training teams in the regionals are multi national (so don't have a clue about the different types of courses) You have modular Grad chief pilots. The legacy carriers with the expansion needed pilots quickly and took on experienced multi crew pilots of any background. They worked out ok.
Bean counters worked out it was cheaper taking experienced guys off the regionals.
The current phase of mentored schemes etc. I have a sneaky suspicion is all down to a tax benefit. This can only be done easily if the pilot is going through the same organisation and the intergrated schools are set up to do this already. There are a couple of modular setups which can do it also eg CTC.
The airline taking you on gets to offset all your training costs against tax, then gets to pay you a reduced salary thus saving on National insurance contributions as well. And to cap it all off they get to claim the VAT back as well but you don't get to see a penny of that.
So for each cadet going through the system call it 120k including type rating they are looking at clawing back 50-60k in tax and vat. Add in the reduced salary and drop in employers national insurance contributions you have a free pilot for 3 years. And you don't have to pay a penny for it apart from a member of staff to oversee it. There is no risk because you have a get out clause at every point so if things do go sour you can just leave the cadet with the debt.