The problem with this is that "the prices are high", on its own, is meaningless.

There is not some ideal price level that prices fluctuate around such that they are "low" when beneath that level, and "high" when above it. That's just not a thing, it's not how economies work.

So what do you mean when you say "price levels are high"? I think what you and I and most people mean when we say this sort of thing is something like, "I have an estimate anchored in my mind for what the prices of things are, and they are currently noticeably higher than that". But where do those price level "anchors" we all have in our minds come from? From recent experience, pretty much.

But by introducing "recent experience" into this, we now have a time component. And that's where inflation - the change in price levels over time - comes in. This is why people immediately start talking about inflation when you say "price levels are high". It just doesn't make sense to talk about price levels without a baseline to compare to, and that is inevitably a comparison between price levels at different times, so now we're talking about a change over time, which means we're talking about inflation, not just price level.

So what I think people really mean by a statement like "price levels are high" is something like "price levels have increased faster than I have mentally updated the price levels I'm anchored on". That is, there is some rate of inflation that gets lost in the noise of our mental estimates over time, but at some point, it becomes noticeable. (And of course this happens at a different point for different people and those people have difference "noise" tolerance across different things they buy.)

Using everyone's favorite bad example of egg prices, if they cost $3 one year, am I going to notice if they cost a nickel or a dime more the next year? That's about 2% to 3% inflation, and no, I'm probably not going to notice; they still cost about $3. But if inflation is closer to 20% for that year, now they cost $3.60, and that's starting to feel more like $4, which is way more!

Then the other thing is that I think maybe we actually should be reporting inflation in longer time horizons. Something I think I've learned from this period is that people don't update these mental "anchors" for price levels symmetrically; we notice more quickly when prices go up a lot, and take longer than that to "get used to" the new level. So maybe it's a 3 year comparison or even a 5 year comparison that would better reflect how people feel about price levels.

For instance, we could say "the 5-year inflation is at about 23%, which is about 4% annualized", or "3-year inflation is at about 16%, which is about 5% annualized". Importantly, you can't directly compare the 5-year number to the 3-year number, only the annualized rates are comparable, but you can see how the long-range numbers each evolve over time. For instance, the 5-year inflation in 2020 was just 9.2% (using this calculator[0] for all of these), which is only 1.74% annualized! This is a huge difference from the current numbers, and I think that has a lot to do with how people are feeling about price levels.

To complicate it even further, I think how people really anchor things - though this is useless for baseline comparisons over time - is not on a fixed time-range, but instead based on the most recent major event, like the pandemic, or the "great recession" before that, or 9/11 before that, etc. You can see that in most of the current discussions on this, where the word "pandemic" pretty much always comes up. We're coming up on 5 years since that, so I think the 5-year inflation comparison captures it well, but we may still be anchoring on price levels from before the pandemic another three or five years from now if that's still the big event we all have in our minds (and I certainly hope we don't have a new one to dislodge it anytime soon...).

[0]: https://www.usinflationcalculator.com/