I worked semi-remotely for a mid-sized company with ~100 IT/developers and those that were working from home were less-involved from a workplace perspective.
I now work for a small company (< 60 employees) that's entirely remote and it works wonderfully. Everyone is on a level playing field and all processes are designed to support it.
You can't expect to work from home and still interact with everyone who is home.
And where is this "someone else" supposed to come from? You have enough money to hire a full-time nanny? For many professionals, both parents work (and the mother taking significant time off to raise kids is a career-killer).
I think you're just grasping for excuses for why working from home can't work with kids.
I don't think I'm "grasping for excuses" at all. The kids that I've seen and met would be completely impossible for me to work at home and maintain any concentration. I'm honestly befuddled how parents of kids under the age of 10 get any rest at all. I guess some of them are lucky and get kids like me when I was young (I was quiet and liked to sit in my room on my computer, or doing puzzles, etc.), but the kids my friends have aren't like this at all, and from my observation are the norm these days (I was an odd, quiet kid even back in those days).
At 3:15PM my father-in-law picks up our 7 year old from school and hangs out with her.
At 5PM my wife gets off work and goes and picks up our 7 year old. I go and pick up our 2 year old.
We come home, make dinner, have family time, and put the kids to bed.
My only distraction during the day is my 4 month old lab puppy who needs a little play time and bathroom breaks.
It's not tough. It's about having a consistent schedule.
I did however get lucky as my 2 year old has slept through the night all but 4 nights since she was 2 days old.
My wife goes to bed around 9PM, I go to bed around 11:30PM, she gets up at 6:30AM and I get up at 7:45AM.