Right. But what if you run out of missiles and BBs? Would chaff be substantial and dense enough to snuff an engine? I've never seen it dispensed---I'm just curious.
Flares would actually be much worse, and probably easier to aim (though still pretty hard). There's a reason we have a "no flares if adversary approaching guns" BFM training rule.
The T-45 engine has to be one of the easiest to FOD out though.