My DH is one of those men who will do things without prompting.
I am not one of those women 
Apparently, there's something which attracts the housework-doers to the non-doers!
(I'm joking. But I do think that a pattern can build where one person does things and the other ends up relying on them and never thinks to use their initiative.)
I use apps and reminders to help jolt me into thinking about the housework. But I probably wouldn't do this if I wasn't aware of what a great strain it would be on DH if I did not. In a massive part, it's mumsnet and other sources like it, when I hear how much of a burden wives of non-doers carry, that it made me think about the burden I am placing. I don't know whether men have this? It's overwhelmingly a female problem, women picking up the slack their husbands and partners leave. Where are the men who discuss the effect it has on their wives? I doubt it happens; it's uncomfortable to discuss your own shortcomings, and husbands who complain about their wife's messiness are met with laughter IME - because people know that overwhelmingly it's the man who burdens the woman. Likewise, I find that when I vent about not being able to keep up and feeling sorry for him being stuck with me, people assume that he has high standards and does less, and I get sympathy for him mistreating me, which makes me feel uncomfortable, that's not the situation. (I appreciate that it is for some.)
BTW, "Fuck you DH" is working wonders. It's not hitting the stuff I don't notice but it's highlighting to me the amount of stuff I always thought I didn't notice but actually I'm noticing and immediately disregarding.
stealtheating - I agree that I find "Well I wouldn't put up with it!" smug bollocks. And yet I do think that these kinds of disagreements can eventually lead to a point where LTB is the only solution, and I have no qualms about telling somebody so, and noting that accelerating such a decision might not be a terrible thing. But yes, it's actually surprising what you find you'll put up with in exchange for other things - security, friendship, love, shared history, a co-parent you can trust. Not easy things to get back. It's never an easy choice to end a relationship and those outside of it should not push - except perhaps in the case that somebody is in danger.