Citi's AT&T Universal Card used to do this years ago, but it's been quite a few years (a decade or more, I think) since they dropped it. That's the only time I myself ran into it on a card from a major banik.

I don't remember whether they called it an inactivity fee, though, or simply an annual fee that could be waived with a few purchases a year (of any amount).

And, with that in mind, there are certainly cards from Citi (and sometimes others) where you can get a retention offer that credits you the same amount as the annual fee if you only make a small number of purchases in the next few months. While if you don't ask for this offer and/or continue to leave the card on the shelf, you have to pay the annual fee (and are never reimbursed it).

So the line between inactivity fees, and annual fees which are only waived for (at least) minor activity, can be blurry.

And the reason the phrasing may be important (including to the bank): Some states may have rules against inactvity fees for certain types of cards (like gift cards), but "annual fees" (and ways to waive or offset them) are typically not subject to the same rules.