I’ve never read any teshuva advocating for the exclusive use of male Ob/Gyns. We’re not Muslim fanatics. We believe “Ve Chai Bahem.”
All EMT’s are more than capable of delivering babies. It’s an important part of their training.
A professional male doing his duties is not a situation of pritzus. Part of why I am not crazy about the “Yoetzet” movement is that the assumption there is that a male rabbi who looks at a bedika cloth or who discusses matters pertaining to niddah is somehow not oisgehalten; it makes men out to be perverts and sexualizes things that are not sexual in these contexts. There is nothing sexual about delivering a baby, unless people’s mistaken ideas make it out to be that way.