But I can't get beyond the arguments made in favour of WOH because they are all about the parents and what they want. Look at your second paragraph. All about being a fulfilled parent. Not what's best for the child.
But that's the point really - what is best for the parent often is what is best for the child. Some parents take time off to be at home with the children, and then find that they can't get back in to the workplace when their children are older. It isn't always that easy - their skills may be out of date, there are gaps in their CVs, or they may simply have lost confidence. For some, this may not be a big deal and they are content to stay at home. For others, it may be devastating.
My mother was happy enough at home when we were small, but she suffered on and off with major depressive episodes all through my teens and early twenties. She was isolated and unfulfilled at home, particularly as DSis and I were getting older and becoming more independent. She deeply regretted having lost her career, hated not having an independent source of income or pension, and believed that she had wasted her potential. She tried to hide all of this from us but failed miserably, and I spent a good part of my teenage years feeling intensely guilty for the choices that she had made, supposedly for our benefit. I often felt more like a parent than a child, and it was incredibly difficult to leave home when I finally did, as I felt awful for abandoning her to her empty nest. I wish for her sake and mine that she had kept her career. SAH just wasn't right for her, and in the long term, it did her children no favours either.
I really would not want any other young person to feel so responsible for the happiness of his/her parents like I did. I think parents must take responsibility for their own happiness and fulfillment themselves, and if that means that both parents WOH, then I think it's a small price to pay.
FWIW, I think it's probably just as damaging for someone to WOH if they desperately want to SAH instead, but I have no personal experience of this. Either way, I'm firmly of the view that happy parents will produce happy kids, while unhappy parents will struggle not to share at least a little of that unhappiness.