Once I left my umbrella at a store, and the next day, I found it on the rack, untouched. Another time, I left my train pass at the bathroom, and then someone handed it in, so I got it again. I count my blessings and Japan can be as safe as the fairy tales, but I would still have travel insurance. Not because it is unsafe, but things can happen outside your control. An international flight can be delayed. You can trip and fall. Or lots of other things that have little to do with safety. So I would always recommend travel insurance. I would like everyone to have a safe and enjoyable time here, and not have to worry because you don't have travel insurance.
To me, the most important thing to make sure your travel insurance covers, if you plan to get it, is natural disasters. Japan may be an incredibly safe country crime-wise and you may never need to use the medical aspect of travel insurance (if you're lucky), but there is a greater chance of encountering an earthquake, volcanic eruption or tsunami here. If those events cancel or delay your travel or affect you in any significant way. that's where I think travel insurance could be quite useful.