Good luck! Most companies are not managed well enough to handle thoughts along these lines.
I fondly remember those companies I have worked for that did think this way. I can assure you we were far more productive than companies that don't think this way. For example, in one company I worked for that developed software, we tended to work about 35 hours a week, and have about 5 hours for whatever we wanted. We wrote experimental code to learn how things worked, we developed concepts that were implemented in later releases, we dove into bugs that we wanted to fix, but that the company had not yet agreed to make a priority.
Along the way, we released 6 versions of the software during my tenure, all of which were not only on time but early! Only one wasn't early, and that was because of scope creep, yet we still hit the original release date!
Another company I worked for not only allowed developers to spend work hours learning new things, it encouraged it. I believe in the two years I was there, I spent almost 4 weeks just reading about and trying new things. Initial hires were put through a rigorous training program, self directed by the way, and were allowed up to 12 weeks to complete that work. Finishing early was fine as long as you hit all of the goals of the program. Senior people graded your work to ensure no shortcuts were taken. There was significant prestige for finishing early while exceeding the goals, especially for those of us who extended what the training application could do. :-D
IMO most companies are too focused on productivity as measured by the day. Make your staff work more hours, don't pay for sufficient staff to allow true breaks for PTO, call them at all hours of the day and night. Companies that do this save in the short term, but drive increased turnover rates, burnout, stress and even violence in the work place. Overall the costs end up being far higher.
Your post may be about "down time", but the root issue is allowing the people you pay to be experts to actually be what you pay them to be. Down time is one solution, there are many ways to accomplish the same thing though. Empower your people (in reality, not marketing speak!) and they will produce more benefit to the organization than you can imagine. Some companies recognize this, but I doubt that most of them do.