David Perell has an essay on the different ways that creative people work. He calls these "beer mode" and "coffee mode". When you are in coffee mode, you are getting things done. You have a list, and you work towards accomplishing the items on your list. Lots of us spend time in this mode every day, and often our bosses expect us to spend more of the time here. This has also been described as "closed" mode.
Beer mode is different. This is an open mode, where we are not focused on solving an idea, but rather playing with something. We are thinking widely, investigating, and not necessarily planning on getting something concrete completed.
For much of my career, I was in coffee mode. I think my ability to take a list and get things done contributed to my success in various positions. I could grind through a set of tasks, even repetitive ones, and show my boss what I'd accomplished each day. Going through a list quickly, even if slightly inefficiently, was often rewarded.
These days, I spend more time in beer mode. Not actually drinking beer, but rather experimenting, playing, thinking, and trying to find new insights into the database world, into how customers might re-imagine their use of our products, and how computing and technology can inspire the world. Those are the fun times. I still get a fair amount of coffee mode in editing, scheduling, etc., but I get more playtime than I ever expected in the past.
We need both types of working. Often we do want focus and concentration. This is where we build skills, develop strong habits, and produce something valuable. This is steady growth. However, we also need creative time. This is where we expand our minds, think outside the box, and how we grow in leaps and bounds. At least, we may. We can't predict when we have a breakthrough or find an "aha" moment, but all of us have them, even when they are not life changing.
Some organizations are better than others at allowing some "beer mode" time at work. If your boss doesn't think there is a need for unstructured work, maybe send them the essay above and see what they think. There might be all sorts of reasons why this doesn't make sense every day, or every week, but I do think that having some experimental time is important for anyone doing creative work. This includes the DBAs and sysadmins trying to get your system to run better without a large budget.