megonthemoon, I don't mind your representation of my work. I don't do the school run and look forward to time time when I can because having an excuse to converse with other adults in RL sounds like a treat 
Back to cognitive dissonance, I think there might (still) be some confusion about what colditz was talking about in her OP.
Cognitive dissonance does NOT engage someone who is genuinely happy in an equal partnership
Cognitive dissonance does NOT engage someone who is angry because their partnership is unequal and who genuinely tries to resolve the situation.
Cognitive dissonance kicks in when the wife realizes (as I did) that her husband hasn't cleaned the toilet in five years, that he doesn't know how to use the washing machine, and he thinks it's acceptable to take off his shirt and leave it wherever it lands - and she excuses it rather than tries to change a situation that is unequal. She makes excuses like "well, he works hard at his WOH job and is tired" "I'm picking up after the kids, might as well do it all together" etc. She does this because she considers herself a strong, competent, smart woman who makes reasonable choices, when her actions are of someone who subverts their will to another person.
The men in these relationships are suffering from a certain level of cognitive dissonance too because not a one of them really thinks they are unfairly loading housework against their partner. DH absolutely, genuinely believes that he does an equal share of the housework and steadfastly maintained that position until I started making lists of the work I was doing. The husband chooses to believe that a) he really does do an equal share or b) his wife is just whining/hormonal/worn out because he considers himself a good husband who wouldn't "dump shitwork" on his wife, who he loves.
It's not people who don't know their own minds, it's people whose actions are at odds with their thoughts / statements. It's the reason you hear people in abusive relationships say that their abusive partner doesn't mean to hurt them.
Cognitive dissonance in the SAH partner absolutely BREEDS cognitive dissonance in the WOH partner because if they get no feedback that they are not doing an equal share of housework, they have no way of knowing how unequal it is without a certain amount of self-reflection that is rare in human beings of both genders.
I don't think anyone has said a certain amount of drudgery isn't required for everyday life, just that working for 8 hours outside the home on five out of seven days per week does not give one a get-out-of-drudgery-free card and when one partner treats the other as though it does, they will have a problem; fights over housework until the balance changes, divorce, or cognitive dissonance. All residents of a household need to share household tasks equally.
I think that maternity leave and the amount of care needed by a newborn sets a very early precedent in a relationship for the amount of kid-related work that gets taken on by the mother. It's hard to change those sorts of habits, especially if one has taken more than a month or two of maternity leave. That's my only explanation for why the balance of housework changes so dramatically after kids come along, even for couples who shared it relatively equally before.
I do believe that there is a preventable societal element, in the sense that individuals perpetuate an unfair balance of roles (ie, MILs telling H's that he's such and amazing contributer to household work because he changes a few nappies, since their husbands did none - well that's setting the bar pretty damn low); but there is also an inescapable societal element in that there is no getting around the fact that women are the ones who bear and BF newborns, so the onus of their care will inevitably fall more on women than men, especially in early years.
I suspect the best way around the whole issue is trying to address inequality in our own, individual lives and in a broader sense, fight society's attitudes that lead to domestic inequality (such as the concept that if a child is dirty/tatty/unfed it ought to reflect poorly on the mother even if they are presently in their father's care). There isn't a simple resolution, and I am quite sad for those who think there is.