> Not to be dismissive, but why would a company specifically care about some arbitrary number called "inflation" vs overall pressure from the labor market, which presumably must have some encoding of that, considering they seem to clearly paying a person enough not to justify leaving?

You hit the nail on the head.

Everything related to compensation becomes much less confusing once you accept that hiring is a market. Like any market, supply and demand drives the prices. Nothing else matters much.

Big companies have entire teams dedicated to compensation which are separate from HR and hiring managers. They carefully track these details and will fine tune their rates up and down depending on how often their offers are accepted or rejected. If every candidate is accepting the offers, they're probably too high and can be adjusted downward. If the company can't close any good candidates because they're going to other companies, it's time to raise the rates.

Of course, not every company plays this game correctly or intelligently. If the OP's company has guessed wrong and gave too low of a raise, they risk losing too many people. On the other hand, if most of the employees shrug it off then maybe they made the right call for the business.