I do wonder if this will have to change when we have children, because we'll need to be more organised about making sure everything gets done in a timely way. I'm not sure. I think we might have to be firmer about doing laundry before we run out of clothes or doing dishes before we realise there is nothing to eat off, but maybe the rest can stay as it is.
Your 'if you care so much, you do it' rule was a problem for us... and then we had children, and it was flat-out unsustainable.
My husband DIDN'T care about the state of the floor, the state of the bathtub, and the tidying, and just wanted to play video games. BUT, if you have a learning-to-crawl child in the picture: they are taking a bath (as opposed to a shower) so a non-scuzzy tub is a plus. If they throw meat off their tray at dinnertime and you don't clean the floor, they WILL find it and eat it 24 hours later (eewwwww). If there's stuff everywhere, they don't SEE their toys, and either destroy everything or become kinda frazzled and harder to deal with because there's too much going on. Like, if it was just me occasionally wanting a bath or clean floors, fine, I'd do them every so often... but it kind of affects an innocent third party too, so get off your tush and help, y'know?
In our case: I'm not a neat-freak, but I'm pretty sure floors should be cleaned before cat hair starts rolling down the hallway in clumps, that the bathtub needs a quick scrub before there are visible rings around it, etc. Functionally, this means that I/we do dishes every night and run the dishwasher, put away our things daily, vacuum the floors 1-2x/week depending on season (kids+mud...), wash the floors and bathroom and everything else maybe every 2 weeks, and do the dusting... erm... every month or two, maybe, when we get around to it. Maybe. Not a huge amount of cleaning, overall, but when it doesn't get done the place gets nasty, and you can't live in a small space and not put things away. We'd fight about that every so often (pattern: I'd do it all. I'd pitch a fit. He'd do 50% for a few weeks. And then it'd start slipping, and slipping, and then 3 months later I'd do it all and pitch a fit, repeat).
What stopped it was when I realized that I was working 50-hour weeks, doing a good 80% of the childcare, running ALL the errands, doing ALL the cleaning, and cooking ALL the food. While he worked 35 hours/week from home. I, erm... lost it. And basically said that this was it, that the pattern was breaking, and that we were FIXING THIS or I was LEAVING, and I MEANT IT (and I meant it. I'd visited apartments, I meant it so bad. It wasn't an aimless threat, it was a 'I am letting you know that this is unsustainable for me; we can fix the situation or I can remove myself from it, your choice'). That was over a year ago.
There's been occasional backsliding, with apologies and acknowledgement, and the housework, outdoor work, and childcare is actually now split in a way that gives us equal free time, which is really all I was asking for. The house is never neat and 'perfect', but it's livable and good, and that's all I'm asking for too. But the fact that it took me hitting the wall and promising I'd leave... honestly, I'm still frustrated that it took that much.