If you're part of a team, the team should be big enough to be resilient to this change (and everyone else should do this too, and your team may need to expand by 15-20%).
If you manage a team, your team should be skilled enough to work without your direction one day a week. If they aren't, you need to step up and develop better procedures.
How many people have come back from a long weekend to a 4 day week and noticed it's just 5 days of meetings/work rescheduled to fit into 4 days.
I'll always remember the stunned response years ago while moving when my wife picked up my cell phone (my hands weren't free) to what was a production trading outage at my firm.. and said we are off today, we are in the middle of moving, we have no internet or computers plugged in. On a 30 person dev team in a 20K+ person firm and we had cross team direct dev team escalation to my personal cell phone because no one could be bothered following escalation procedures/rotas/call lists/etc.
My fear would generally be taking the 20% pay cut and not really getting 20% less work/time expected.
My company treats it the same as vacation time. On the occasion there's something that only he can do but he's not in, it'll have to wait.
He is a "regular" salaried dev on a medium sized team.
I think probably 60-70% of the places I have worked, this sentence " On the occasion there's something that only he can do but he's not in.." would end in "we call his cell".
I was just on a medium-urgent outage the Friday before Memorial Day weekend and 2 teams on the call were calling their on-vacation colleagues for help.
The only day I could see plausibly doing this is Friday as there are few meetings and lots of senior people WFH/use remote offices then. Of course this also means taking the easiest day off!
How did you make this work, is it a consulting role? Individual contributor? What is the off day, Friday?