It probably helped that I convinced them (then proved it) that my productivity really wouldn't fall much. I could do the same work in less time.

Unless you're making widgets on a production line, productivity doesn't linearly scale with time.

I wasn't at work on Friday, but I was still subconsciously processing what I had researched, how to solve problems, etc. It's the ultimate "sleep on it" or "get up and walk around".

Did you experiment with other days, or was it just Friday? Was this choice made by you, or what fitted the job the best?

I didn't experiment because I felt it was unfair for my availability to wander through the week. People learned I was not present on Friday.

I wanted it to abut the weekend so that I could get into my own projects (coding, building, being with family, etc.) for a longer amount of time.

Things managers really hate to do, #1: Ask superiors for a budget increase.

What tends to kill these kinds of arrangements is other employees complaining and wanting the same deal in my experience. aka the "NO FAIR BILLY GETS TO!" factor

I think mature managers and mature employees makes this go away.

The world could use more of those for sure!