I'm not too sure about the 1st and 2n class moms.
But here's how the system works. It depends on when the mother delivers. If she delivers during standard working hours, there is a higher chance the mother would get a doctor or a specialist to do her delivery. Because...they will be around.
When it's pass working hours, most of the specialist and medical officers go home. Leaving the housemans and medical officers and a single specialist who is on call.

It seems to me that you may have a bias against midwives. Correct me if I'm wrong. But assuming you do have that bias.
It's a very misplaced bias. Midwives conduct better delivery than doctors.
Let me explain.
Doctors serving in the government hospitals usually hop on to private hospitals later on. And those who do stay, do not manage as much deliveries compared to the midwives.
Midwives in government hospitals have MUCH MUCH MUCH more experience. And they have been conducting so many deliveries day in and day out. I'm so convinced that they can do so with their eyes closed.

Those who go through the emergency room can be of two types of mothers.
1. Normal mothers with normal pregnancy - higher chance of being delivered by midwife (that also depending on what time she comes through the ED)
2. If the pregnant mother has complications for example; seizures or bleeding per vagina, she will definitely be attended to by a doctor.

The chances of getting a pregnancy after a bilateral tubal ligation is 1 in 80
whereas using intermittent methods? 1:200