There isn’t. The word inflation represents many, including wildly divergent, ideas.
And many of the very different things represented by inflation serve very different purposes, and that’s why they’re changed, because different measures of inflation help measure different concepts. Core inflation is just one of many different measures of inflation.
And not the main one produced by the BLS. Core CPI is the headline CPI with several items removed.
If OPEC decided to stop producing oil altogether you bet there would be “inflation” caused by oil prices but that doesn’t mean the FED should be goaded into making changes to policy.
It doesn't, it produces many different Consumer Price Indices, plus a variety of industry-specific Producer Price Indices, all are measures of inflation.
Why should not? Inflation is just change of price level. Price level is just ratio of circulating money to real production. If OPEC decided to stop producing oil, that would create massive negative shock to real production, so FED should restrict circulating money to maintain that ratio.