I think what you seek is a great companion to truly share the responsibilities with.

I am a father of two wonderful kids. I do more drop offs than my wife, I changed just as many diapers / handled sick care, I handle more of the nighttime routines and give each kid a 10 minute back rub every night while my wife lays in bed (9 years and counting for my eldest) and cook more than my wife. She does clean more than me, folds more laundry, prepare their lunches, organizes their after care and play dates and babysitters more. She also worked harder when the kids were 0-6 months than I did for sure.

I begrudge her for none of what I do “more”. It’s hard work but I love being with my kids and my wife works her tail off running her business. We have a great balance and I feel lucky. And yet life isn’t perfect and, it being hard work, it’s easy to point fingers instead of focusing on gratitude and real world trade offs (two things the paper and feminism generally lack).

I think it comes down to ambitions. Do you have ambitions to be financially successful, to have a wonderful career or marriage or to be a great parent? Although feminists are loathe to talk of hierarchies for obvious reasons, they nevertheless have their use. So let me hierarchize: I truly have greater ambitions around being a parent than anything else. We also happen to be financially successful (more so because of my wife) but she has greater ambitions around that than I do.

So anyway, I think we are the counter example to your last statement and show that it can be compatible. And many of my friends are similar.