The BoJ measures inflation to help it manage the economy. It’s not a political tool. As an individual, changes in your cost of living are personal to you. You don’t need the central bank or the government to tell you about it.

Obviously, the BoJ isn’t focused on individuals. It wants to see what’s happening across the whole economy. Through research that is freely available, it has determined that the index provides a more reliable signal when volatile fresh food prices are excluded (because the things that typically cause these prices to change, like the weather, don’t reflect a broad shift in the economy).

You’re wrong that energy isn’t included. That sentence is referring to a different (“core-core CPI”) index, which is higher at 4% because energy prices have gone down. Japan’s energy problems are as result of the post-Fukushima shift from nuclear, largely a result of public opinion.

Put simply, CPI isn’t a measure of “cost of living“. It’s a tool for central bank policy.