I do agree it isn't so much an unschooling issue as a parenting issue. It's just sometimes tricky to figure out how to make it happen... There are plenty of people with schooled kids that wrestle with getting their kids to do chores. But the kids aren't home so much of the day. And the parents don't usually over think whether it's ok to ask/require help.
Personally, I refuse to do things to an extent that I feel like I servant. I'm happy to help a child that needs help. And I'll help a child who simply wants help. But I'll also let a mess of someone else's creation sit as a way to let it be known that I'm not responsible for it. Sometimes things don't happen as soon as I'd like (unloading the dishwasher, for instance) but I don't just empty it because it's more expedient. My family eventually notices the lack of clean dishes is a problem. Dh knows I won't cook as much if there aren't clean dishes with which to cook. Ds likes to use the regular spoons and isn't happy if the only thing clean is soup spoons. My ds has occasionally told me something it dirty/messy and that I should clean it. I laugh and offer to help him clean it.
I think the OP also has a difficult age range of kids. The oldest doesn't need so much help but probably wants some. And probably doesn't feel like she should do more than the younger kids. The younger two (6 and 4) need more help and direction. And possibly the OP has a greater need for things to be clean and orderly than someone like me. Also, my ds is a bit sensory averse and appreciates when things are clean so he does eventually notice when things have spiralled too far.