TLG is a different game, with different priorities and a different mission.
Some of Team ICO's main focuses are animations and draw distance, two things that the Bloodborne engine doesn't handle well enough for their standards. I mean... to this day, I can't think of any game that feels quite as alive as Shadow of The Colossus did.. "a PS2 game".. why have a team of this level of talent barrow an engine from another developer? Yes, they were struggling.. the PS3 proved challenging to develop for and their target was too demanding for the system. But luckily this is changing with the PS4 and Shuhei Yoshida said the team is making a great progress..I'll take his word on this one.
I believe it's better for a creator to build his/her own engine and have things their way with no restrictions hindering their ideas and forcing them to adapt as long as they are capable to make engines.