I’m not sure that I agree. I gave birth in America x3 and in Israel x3. In America I was able to have my sister be there with me. The nurse was basically the only one in the room for the vast majority of the labor and the doctor only came in when I was really ready to deliver. In Israel, there was a midwife and the doctor came in to observe the actual delivery. I had no family who could be with me and my husband was not going to be in the room under any circumstances once things really got going. I did not want him to see me in pain and he couldn’t touch me any way, so what’s the point. I did, however, want someone, who could hold my hand, run and scream for the doctor/nurse or someone to help me when I ran into some problems, etc. A doula knows how to work with the staff in the hospital – you can ask which hospitals the doula has worked with before (if you are taking a frum one versus one that works only with the hospital you are going to). They are also available to help you at home beforehand, which can mean less time spent at the hospital as they will not likely tell you to run there before it appears to be necessary. You can call them when you think things are starting and they can assess the situation even on the phone and give you advice or decide to come over and evaluate more thoroughly.
In short, I strongly recommend doulas no matter what kind of person is going to be delivering your baby. It is in your wife’s best interest (I am assuming Dovid HaMelech is a man).