I barely see/interact with my kids on an 8 hour day. On a 10 hour day, I'd probably miss them completely.

I would like one day a week when I'm not working OR looking after the kids, however. That would be amazing. It would be great to give it a try and see how it worked out. Unfortunately my employer is a hardass and doesn't even allow work from home, let alone fewer days a week.

Young kids need 10-12 hours of sleep. 10 hours working, plus 1 hour lunch, and a 30 minute each way commute means your kids likely should literally be sleeping the whole time you're at home during a work day.

I don't know any parents that do that - literally never interact with their kids 4 days out of the week. What actually happens is parents sacrifice their kids' sleep schedule.