While we're speculating, perhaps U.S. consumers more directly correlate price with quality and would be leery of prices that are "too low." A $1 fare? There must be a catch.
So on that note, a $1 promotion would work against the high quality, low fare image jetBlue is trying to promote, whereas AirTran might be wary of looking too cut-rate lest the media bring up ValuJet Flight 592. Southwest doesn't need such promotions when it already has a well-established low-cost image, and $29 each way promos work just as well. But I could see this gimmick tried for an outfit like Hooters Air.