You are absolutely right.

The cost of living is not that helpful by itself. It's only the "cost", doesn't say much about the quality nor its actual affordability.

Not to mention expensive places are usually expensive for a reason, good economic activities, meaning more public service (usually) and employment.

inflation also has this vagueness/misleading as well.

It's about the cost to maintain the same quality of life.

While everything is getting more expensive, we have more choices, we shift our preference, while most things also have shrinkflation

And preference sort of influenced by the price tag as well, there's a bit of a loop there.