Wow, I love this discussion. I may have the opportunity to stay home (dad here) by next year with our then toddler son and hopefully a future child. We won't be FIRE, but my wife has the better career and is inline for a big promotion with lots of stability. It wouldn't replace my income, but is more than enough to live on and pay should increase with time. The problem is it's a demanding job, and hard to juggle, especially while I'm also working a medium stress full time job. Most of the husbands of women in the same role as my wife at her work stay at home to help balance it.
I was actually off for 4 months this year due to a generous company leave policy with my infant son (5 - 9 months), so I know how isolating and tough it can be. However, in many ways I enjoyed it more than my desk job, and it certainly felt more rewarding. Our lives were also a lot easier, since I was able to cover most of the household labor instead of cramming it in and outsourcing like we have to do now. Our son seemed a lot happier too.
The problem is, it's hard to walk away from a good job, with a good salary, benefits, and flexibility (WFH 2x a week). It would also set us back towards FIRE. I also feel like SAHDs are judged pretty harshly, and it would be tough to jump back into my current career (ad tech) since it evolves so quickly. It feels like a lot of personal risk, like if something were to happen to my wife or our relationship, and that makes me nervous. It also drastically changes the power balance in the relationship. Ideally, I'd work 3 - 5 more years to increase our savings (particularly tax advantaged accounts), but at the same time these early years are the most crucial for our children, so that may not be the best option for them.
The way I'm trying to think about the possibility is sort of a part time FIRE. I'd escape the corporate grind with plans to hopefully not return, cover the bulk of our domestic labor, simplify our lives and expense for the next 5 years then work my way back into some flexible, part time gig once the kids are in school.