You're half right. In a sense, food and energy should be included, but the problem is that they're much more volatile--you'd reliably have a huge surge of inflation in the US as gas gets more expensive in the summer, and deflation in the winter as prices go down. This would make it much harder to understand the numbers you were seeing.

"Core inflation is 4%, which is high" is understandable, "Inflation is -1%, but that's actually bad because it's November" is going to make communication basically impossible for non-experts.

I've always thought there ought to be a way to do some kind of damped average, so that you can detect "food has been rising in price for the past few years", but ignore "gas prices surged after memorial day", but it's hard to think through the details and find something that makes sense.

Jobs numbers work the same way, btw...we adjust for seasonal labor.