men are meant to participate in the "traditional" roles of cooking and cleaning, but all of the traditional male roles like maintenance are still performed by the man

Meanwhile J does all the cooking coz he actually enjoys it and I really don't XD

_{also I'm reasonably certain I could set water on fire in a kitchen}

After forcing everyone to at least have a working knowledge of the basics of how to run a house much to their disgust the chore division is just to everyone's strengths/what they hate least and is not equal in any way, shape or form. Which means J does most of the cooking with youngest doing some and the bigs even less, I do all of the laundry except for the kids' bedsheets (supposed to be their problem but sometimes it just ends up in the laundry room and I do it anyway -_-) and most of the cleaning and occasionally bully the kids into helping me (eldest is best at helping but may glitch out and wander off before completing all tasks, middle is extremely selective about what she will and won't do but does the stuff that she will do extremely thoroughly and amazingly, youngest goes out of his way to avoid cleaning but seems to think he does a lot more than he does) and the boys (including J) do most of the maintenance and outdoors/gardening work. Middle does stuff when home and able (she and her boyfriend are living between our houses, he helps too when given something to do).

there is an expectation that men should appreciate the tasks women do, but women can expect men to do their work without appreciation

I've mostly noticed the opposite while wandering through uni and a short distance beyond, where men don't seem to notice anything that women do at all but expect a parade because they did something super basic that one would normally do in normal household operation.

men are somehow unaccustomed to doing housework, and that they all grew up in some kind of home where their mother coddled them

Maybe they're these guys XD

She has also never sawed a branch of a tree, nor has she carried a wheelbarrow full of earth. She just can't.

Can understand the axe thing as I'm pretty nervous about swinging those and that coupled with not being that strong means if you want the wood chopped this century get someone stronger to do it. Those other things are not as hard though, she can't be that much smaller/weaker than me O_O

If I were to just stop doing anything though, perhaps it would highlight what actually gets done

Good luck with that XD I've gone "on strike" many a time and all that happened was the bathroom and kitchen became health hazards and the (clean) laundry piled up (because while I still washed and hung and brought it in I refused to fold and sort it) everyone very astutely refused to mention it because the last time (several years ago) anyone said anything I told them to do it. Didn't change anything.