I imagine that if we all worked 3-hour-days the price of housing would massively reduce, as rent and purchase prices can only be what the market can pay, and that goes for the land they’re built on too. I doubt this would be a perfect 1-to-1 match to income changes, even if it happened in every country at the same time.
We have a housing cartel ensuring the supply of homes remains lower than demand in areas with decent jobs. So the person who wants to work a 3 hour day can't compete with the person who says "well, I'm willing to work a 5 hour day to afford a home, at least for now".
Of course, in reality it often comes down to the person who wants to work a 40 hour week competing with the workaholic who works all weekend on a regular basis.
Similarly, a lot of couples might prefer to have one partner stay at home and do childcare, but this is impossible (except for the rich) with a housing shortage, because homes will always go to the wealthiest (usually those willing to be two income full-time households).
Once you have 100 households seeking 101 homes instead of 90 homes (etc.) it _does_ become possible. When you're competing with "I'd like a bigger home" vs. "I need any home at all" it gets easier.
"If we all worked 3-hour days" is an imaginary situation that doesn't reflect the fact that a ton of people are immediately going to attempt to outbid each other by working more, though.
Hand waving it away with some sort of "but all the prices would reduce" assumes some sort of co-operative prisoner's dilemma situation.
I would immediately defect, take two jobs, and have twice as much as anyone else. Most people I know would.
Seriously though, as with so much else in economics and politics, there are many more things that need to be determined than just a nice end-state. That doesn’t mean the nice end state isn’t nice or worth searching for routes towards.
