Both of my girls were born with me on my back, DD1 i didn't really have much choice but DD2 i got into that position for the nurses to check me and she asked if i wanted help moving again and i said no i need to push, i'm not moving.
I actually wonder if my girls could have been even quicker had i been on my hands and knees or kneeling, but with 8min pushing DD2 on my back i'm not sure i wanted any faster