I don't think anyone here is trying to say a live baby isn't important, of course it is. But if you could have a live baby (more likely with a smooth birth) and a relaxed and happy mother, then why not have both, it's not an either/or choice.
Someone upthread asked what the job description of a doula is. It's a really tough question, because there is lots of things, usually people describe it in vague terms (providing practical and emotional support) or in terms of what they don't do (give medical advice or perform medical procedures).
To give you a rough idea... Before the birth, doula visits parents for at least 2 long sessions, but possibly more, and will be available for phone support. They will discuss birth plans (although doulas won't give advice, they can give information, so if the parents want to know about say, why delayed cord clamping might be a good plan, or the risks of induction, she should be able to provide the information, or a source for the information). In the ante natal visit the doula will discuss the mother's previous birth experiences and expectations, help her debrief traumatic births etc. They might talk about breathing techniques, might teach DH useful massage techniques. Some are also qualified in complementary therapies. Ultimately they are there to support your choices, so if you want a basic hospital birth, that's great, if you want to give birth in a yurt to the sound of tibetan bells, then that's great too. There is no judgement.
During the birth the doula is there to support both the parents. She won't tell anyone what to do, but she can advocate via the birth plan, someone mentioned a woman in stirrups upthread, the doula could explain the the medical team that the mother wanted to birth in a particular position, and ask if her wishes could be accommodated. Doulas usually know the local midwives and are, as someone said, in their "workplace" so are less likely to get swept up in things and forget the mother's wishes, or be shy about asking. Doulas are experts at keeping the "bubble" around a woman, so she can focus on birthing without distraction and the stress it causes. They can remind DH about how he can support the mum. They can also "translate" and explain what is happening if things go "off plan". A doula will not leave her client during labour to change shifts, she is there for the duration. Ultimately there is good medical evidence that shows the presence of a doula improves the health of mother and baby.
Postnatally doulas help mums get used to looking after baby, help with older siblings, they might cook meals, run the hoover around, or look after baby so mum can have a shower. Different doulas will offer different services, but generally, it's like having a female relative helping, but one who will support all your choices 
There has been talk of cost here too, so it should be said, mentored doulas, who are newly qualified are much cheaper, and if you are on a lower income, Doula UK have an access fund to subsidise the cost of your doula.
Hopefully that clears up some questions.