I think context is critical here. You have some great stay at home parents, and you have some really shitty ones. People often have vastly different experiences in this area.
I had a stay at home parent that I'm fairly certain I can state had serious depression / mental issues that were untreated (though I didn't understand this as a kid). Their average day consisted of watching TV all day.
I rode an activity bus home (extracurricular band related activities) twice a week from a school that was 7 minutes away from home and it took me 1.5 hours to get home because it went the opposite direction first.
I was forced to quit band because during the marching band season, a Friday sporting event and a Saturday contest was "too much work". Let me tell you, its hilarious to take an awkward fat kid and remove socialization and exercise because its inconvenient for a parent.
I had to beg to go to the library, which again was very close to home. You'd think parents would kill to have a kid that wanted to go to the library but nope.
I didn't get a license until 19, and only then because you pretty much need one to have a job. I'm to this day the only person I've ever known to have been forced (by my parents) to voluntarily surrender my license - the insurance company tried to up the premiums for car insurance, and the insurance company agreed to drop the charges if I surrendered it.
My stay at home parent resented how life turned out. Resented having children. Every time people start talking the "its the hardest job in the world!" talk, the only response I can come up with is "Any job is a fucking cakewalk if you don't actually do it".
I never suffered physical abuse, but it was an environment of fear and discontent. I'm closing in on 40, and one of the thoughts that I've had recently is if I'll be able to manufacture any reasonable response to the eventual death of my parents because I hate one and I don't know the other because they worked 90+ hours a week and were only off while I was at school.
They've completely alienated my dysfunctional sister fighting over who the grandchildren like more etc. They have destroyed their relationship with my fathers mother (no other known family), and I've never heard anything about family period on my mothers side. They have grandchildren they haven't seen in 5+ years as the culmination of a Jerry Springer worthy story. I maintain a relationship with them much like you'd have with a business acquaintance that you might need in the future to provide a reference.
TLDR: Many of us didn't have a great experience with their parents.