EI will only handle them if it's cost effective for them to do it, they dropped EY for this reason.
Same group so different costs attached. BA binned third party handling at LHR years ago but they hande Iberia at LHR in the same way Iberia handle BA at MAD. As schedules are enhanced to bring the airlines closer together, they attempt to get the customer experience to be as seamless as possible. Effectively they'll operate as one carrier so having BA in a different part of the building is something IAG
will be looking to address, if possible and practical. Big IF that one