The only way to prevent this happening is to not engage in it. Men are perfectly capable of doing this stuff when they have to. When I met my H he was a single dad and he coped with all this stuff perfectly well. I worked and he didn't, so he did all the cleaning and cooking plus school drop offs and pick ups.
In my last LTR, we moved in together after about a year and it became apparent that his ex wife had done almost all the wife work as he was completely disorganised. One morning he asked me "Why haven't I got any clean shirts?" and I replied "Well I'm just guessing, but I'm assuming you've made all your shirts dirty, you didn't put them in the laundry basket, so they haven't been washed. I'm off to work, see ya later." He very quickly managed to train himself to actually take some responsibility, otherwise he was going to go without meals, run out of shirts or constantly have creditors calling asking why he hadn't paid the bills.
Men abdicate from this responsibility because we let them. If we want to change things going forward, we have to teach our kids that it's not women's work and men's work, it's just work.
And yes yes yes to teaching girls practical household tasks. My dad taught me to lay bricks, change a plug, rewire a car stereo, use a lathe, a jigsaw, a hacksaw, all kinds of tools in fact. Funnily enough none of those jobs required a penis, just as vacuuming the floor doesn't require a vagina.