I thought about this myself as well. To me a 20% reduction in work days is well worth a 20% reduction in pay. This is an easy perk that is offered at no large companies.
Sadly it's not widespread. And I fear most companies wouldn't be well prepared to actually execute on it.
In the UK, it's certainly worth trying. Apart from purely the fact that places may prefer to keep you for 4 days rather than lose you, employees have the right to request part time work (amongst other things). Businesses have to give a reason if they say no, and the reasons get harder to justify typically as a business grows. Not guaranteed, of course, that would be rough on all businesses but it's certainly something that should be taken seriously.
At $75k/year $15k for a day off a week would be roughly "break even" on the hourly rate trade off.
Someone on $100k taking a pay cut to 4 days would see their time valued at an increase in hourly rate. Since you're getting 15% less money in exchange for 20% less time.
Broad brush strokes on the math there but you get the picture.
Being self-employed, I have to make that choice -- "How much value is a day off?" -- every time a customer asks me to take on a project. Converting a 4-day week to annual vacation: 1 day in 5 is about 50 days off the standard 250-day work-year. I'd pay a whole lot more than $15k for 10 weeks off.
