Assuming the income stays the same, I'd happily swap places. I suspect many people would.

There are 2 further points:

1. I'd say the ideal setting is for both parents to work and hire a sitter even though it might financially net the same (or affordably negative) as having one stay-at-home parent. Because a human needs community and diverse things to do, not just one thing over and over everyday for years. Both of the parents will be much happier.

2. When people say taking care of baby/toddler is difficult, it's almost always about not eating well and/or not sleep well. Eating would take an hour of spoon-feeding because the kid wouldn't eat by themselves. Kids wouldn't be able to sleep by themselves. You must focus on solving these 2 areas first. Once they are solved, it gets a lot easier to take care of a baby/toddler.

While stay at home parenting isn't, and shouldn't have to be, for everyone, it also isn't somehow a downgrade from being in the working world. If anything is doing something 'over and over', it's trudging to some job to push papers/keyboard keys around for 8+ hours.