I think you're falling into the old trap of hoping for a single metric to perfectly sum up a complex situation. As is often the case, no single number does that. The price changes of everything get tracked and analyzed and used for various purposes. Looking at different areas separately can tell you different things. You can go look up how houses, food, and gas prices have changed - nobody is concealing this information from you. But if you want a number that perfectly summarizes inflation, you're simply looking for something that does not and can not exist. Inflation is complex and happens for different things at different rates.

So, yeah, some metrics exclude some things so that they can better see the other things. That doesn't mean that the excluded things don't matter, it means that whatever metric you're looking at just doesn't include those things. If you want to see an inflation rate including those things, look at an index that includes them.

If you look at food and energy over long periods, they work nicely.

The catch is look at something like eggs in the last few months. Was the doubling of egg prices evidence that prices across the board were going up, or was it an anomaly that corrected quickly? We'd be foolish to think that we were looking at an at large inflationary trend when they went up, or conversely, that there was a deflationary trend at large when they came back down.

Yes but that makes it possible to appease people with lower sounding numbers(even tho they now don't really mean anything anymore) and that's something interesting to the ruling