On the Tighten blog Samatha Geitz sums up the benefits of giving developers one day of "free" time a week.

About a year ago, Tighten officially implemented a "20% time" policy for its developers. This means that, on any given week, we only bill our clients for 32 hours of developer work; for the other 8 hours, developers can work on whatever projects they’d like to (as long as they can readily come up with an explanation of how it benefits the company in some way.) ... Here are some reasons that you may want to consider experimenting with a policy like this

https://blog.tighten.co/give-your-developers-20-percent-time