There's no annual fee the first year on the typical Citi AA credit card offer, but making just "a purchase every couple months" won't get you any bonus, since the typical Citi AA credit card offer these days (that has any decent bonus) requires something like $2500 or $3000 of spend in the first 3, 4, or 6 months of the card to get the bonus.

And thus it's not a "brainless" decision to go for one (or especially two) of these cards these days. You have to be sure you can meet the spend threshold in time (and twice over if you're doing the trick of applying for two at once, in order to get two bonuses every 20 months instead of just one), or else it's not worth even bothering (because you'll lose your only chance in 20 months all for nothing).