I have the feeling that several of you are in the UK where the system is different (correct me if I’m wrong). In the U.S., most midwives are in practice with OBs, who are supportive of these midwives, otherwise they would not employ them. The midwives who would attend a planned homebirth are not the type who would even want to work with OBs. What sometimes happens is, a woman is planning on using a homebirth midwife, who isn’t even welcome in the hospital, and so the mother also has an OB who she goes to for monthly checkups.
One day the OB gets a phone call that oops!, the woman gave birth at home, because she was just laboring her heart out at home and suddenly things “were going too fast and there wasn’t time to get to the hospital”. But if things seem to be heading south at home, they will transfer to the hospital the OB practices at, with the homebirth midwife along as a “friend” or “doula”. (Which she would certainly be qualified to do anyway) The mother doesn’t really care if “her” OB is the one on call, because she is only there because she needs the services of the hospital.
The philosophy is like, you don’t need a plastic surgeon when a bandaid will do.