I for one feel stereotyped and vilified (and I also feel at risk of being criticized for even admitting my own feelings).
What I'd recommend the author do is-
1. Reflect on her feelings. What does she really want, what is it really about / a symbol for (cleaning/initiative = caring?) ? Also understand any accumulated frustrations that may be coloring things.
2. Try to understand her husband's feelings, as well as any of his accumulated frustrations.
3. Ask him and make sure you understand his feelings. To do this, you need to be able to listen without judging what he has to say, even if it's hurtful. Once he feels understood, you'll be half-way there.
4. Talk to him about your feelings (does he not notice, not care, or something else). If he's uncomfortable talking about this, that's another thing you can't ignore and steamroll over, but should investigate gently. Hopefully he can understand your feelings without judging either.
5. All 4 steps above depend crucially on sincerity, good-fath, a sense of humor, and tact.
As an aside, I'd never consider publishing a criticism of my relationship online (nor would I use an anecdote as the basis for a gender-criticism), unless I had talked it over with my partner first and they read the whole thing. Of course everybody is free to share their experience, but wouldn't people naturally be hesitant to date somebody who uses intimate challenges as career-fuel?