On an AONEx you may choose to fly a class lower than A. On many routes, of course, A is not offered and so you must do that. But if after booking an A segment the airline inconveniences you in some way - e.g. by substituting an aircraft without enough first-class seats, or heaven forbid overbooking the first class cabin - my experience has been that if you whimper a bit you'll receive a little compensation. AA's dole seems to be 8000 FF miles. CX has been noted here as being much more generous. Those are gifts, not perks.