I have a job which is very technical, requires a lot of concentration, and is safety critical. I cannot do it on consistently broken/inadequate sleep. Not all jobs can be done on autopilot.
More generally, going to work sleep deprived is hellish, you're on someone else's schedule, you have to perform, and you have to endure a commute, which if done by car puts both you and the other motorists in danger. Driving sleep deprived is like driving drunk.
During maternity leave I was beyond sleep deprived and it was really hard, and at times I felt very bleak. She was EBF so only I could do night feeds.
However, all I had to do in the day was schlep to a baby group or two, mind the house, and do the shopping with a small baby in tow. While not 'easy' it was nowhere near the responsibility of work and driving, and I didn't need to be mentally switched on so it didn't really matter that my brain was operating at 40%.
My husband did his best to support in any other way he could, and did loads in the evenings and at the weekend between feeds to give me some rest.
Now that I'm back at work, any night wakes which may happen are dealt with evenly, and we work together as a team to make sure the other gets the rest they need to go to work, do a good job, and put food on the table and keep a roof over our heads.