Honestly I disagree that it's bad advice. The advice I give to a lot of new dads specifically is that Moms #1 job is to take care of baby, Dads #1 job is to take care of mom AND baby. Even if the little one is formula fed, the weeks/months after childbirth are so difficult for mothers. Sacrificing yourself a bit, in my opinion, IS balancing the work.
As time goes on and you have a toddler, things even out significantly.
Mom's job is not to sacrifice herself to take care of the child. She must both preserve herself, go through the healing process, and help take care of the child.
Dad's job is to also handle any healing, to help take care of mom, to help take care of the child, and to generally keep the house functional.
If Mom kills herself taking care of the child or sacrifices herself to take care of the child, that isn't functional. Something has gone wrong. If Dad has to sacrifice himself to take care of the child or the mother, something has also gone wrong.
You must _integrate_ the child into the family, not replace the family with the child. It is not just what works best for the child - it is what works best for the family as a whole. The child would love to constantly breast feed and comfort feed on mom forever - that is not functional for the mother, she must sleep and have time with the child off her nipple so she can continue to breast feed.
In the same way, it is not functional for dad to say, spend all his time cooking and cleaning and not sleeping. It is better for dad to sleep and some of the chores to go undone then it is to have a tidy home.
If you sacrifice yourself - if you spend and spend and spend - you will see it as a debt accruing that will never be paid back. You will breed resentment to your family. You will be unhappy and the family will no longer be a family. That does not work. It does not matter if you're the mother or the father, self sacrifice destroys families.
The family has to work as a whole. Everyone has to be integrated and the system has to work as a whole. What that looks like differs for every family and is an ongoing process, not a one time solution. The father and the mother have a relationship, and now baby is involved which means we went from 1 relationship to 3 (the baby has a separate relationship with each parent!). The family has to make that work not for a week or a month or a year, but for the rest of their lives.
As time goes on and you have a toddler, things even out significantly.