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.
Sadly it's not widespread. And I fear most companies wouldn't be well prepared to actually execute on it.