This can be resolved by choosing a better man as a partner, one that is supportive and willing to be an equal partner. I understand finding someone that fulfills that as well as this person also being someone you're attracted to and compatible with socially is challenging, but I have seen relationships like this before so I know it's possible.
And then there's the fact of life that other stuff needs to be taken care of. Trash still needs to be taken out, groceries bought, etc further pushing you towards the stuff outside of parenting.
This can hardly be resolved with money. We could hire nannies, get the top nursery, whatever. It would even be cost-efficient if it let mom work. However, the kid doesn't want to be without his mom and much more so she doesn't want to be away from him for a longer time! Even with me 4-6 hours is about it.
I am sure children benefit from having several parents and role models, but I am not so sure that the shape of the genitals matter as much as whether the parent(s) is/are emotionally in tune with the child. The classical father of yore was simply not much of a parent. Today's can choose either.
Your child might want the mother, but this is no true of every child. Different kids in the same family can be different in this way too.
Who told you these are jobs you can't equally share with a partner?