I think it is great to involve the kids in housework. Mine did their part as they got older. I think involving the kids is even more crucial in large families, but is good for all kids regardless of family size.
Maybe her ideas about herself are idealizations. Or she sees her ideal self in other families. I do know of parents with large families who balance things well, but I don't have that skill.
Thankfully my H stopped doing this, but he would bring up a friend, who had a large family, who seemed to have it all together, and still looks amazing. But we would only see this couple out at dressed up events. I told her that my H thought she had it all together ( I think she does ). She laughed and told me to send him over when things were chaotic and she was in pajamas yelling at the kids!We don't see everything that goes on in other peoples' lives, but your wife may only see these families all dressed up in church looking great there.
I am not a good housekeeper, but the kids are well cared for, and I am a great cook. And if the job is mine- then I get to decide how to do it.

You do too.