A number of commenters on my initial post believe the chained CPI just disguises the decline in well-being when people make substitutions to less desirable purchases. I don’t think so, but I think the impression comes from the canonical example: if the price of steak rises, people will buy more chicken, and that makes the chained index grow more slowly.
But substitutions don’t have to always go from more desirable to less desirable goods. That’s why I used this e.g. earlier: if the price of steak falls relative to chicken, shoppers might buy more steak and less chicken. This is true even while the price of steak remains higher than that of chicken (though the difference between them is less than it was last month).
The chained index tends to grow more slowly not because people are always switching to absolutely cheaper goods, but because they’re responding to declines in price changes in one good relative to another.