Speaking as a working parent (married to another working parent), it's worth pointing out that this dichotomy isn't mutually exclusive:

raising children is far more self-fulfilling than working a job could ever be for most people.

I agree with this! But I also would note that of the 168 hours in a week, being away from them for 50 of them (especially if they're at school anyway for 30 of them) doesn't really detract from my ability to do both big picture parenting (teaching life skills, moral values, building memories, being a role model) or even the small stuff that adds up (cooking meals, helping with homework, listening to them, talking to them, taking them to and from extracurricular activities, pursuing hobbies together, etc.).

So it's not an all or nothing thing. Most working parents can still raise children in an immensely fulfilling way, so the fulfilling part of a stay at home parent isn't actually exclusive to the stay at home parents.