I don't know, I understand your points about the pilot's processing workload - and how do you best break through that to get a priority interrupt (to continue the microprocessor metaphors!) - but you have to consider the controller's processing status as well.
While she may not have been in a particularly high-workload situation, you have to grant that this was an emergent situation for her, and at the time she was keying her mic, she was still ramping up in the very early stages of analyzing, processing, and reacting to the situation herself.
hear urgency in her voice, and I think she got it right for several reasons:
(1) As she was probably still analyzing, and processing this emergent situation even as she was starting to react (speak), she had to keep control of herself and her own voice; if she stumbled, screeched, or yelled (possibly overmodulating the transmitter and rendering her transmission harder to interpret), then her one chance to get the information communicated in a timely way would have been lost;
(2) I believe the first words out of her mouth were the right ones in this time critical situation: "Go around, Go around..." In an emergency situation, she got out the command first, clearly, and then repeated it quickly for urgency. Both the repeat and the cadence of her speech sound urgent to me, if the pilot didn't break off an interrupt thread based on that, I don't know that raising her voice (I assume from your all caps and the exclamation point) would have helped much more;
(3) As far as putting the aircraft ID first, the only aircraft on final and subject to a "go around" command was the subject aircraft. As ride suggests, on final, one should always be ready and sensitive to a possible go-around trigger, whether from your own processing, or brought in by tower. Once she got the initial "Go around" out there and repeated, and as she continued processing, she did indeed put his ID on there, and then repeated the "go around" again. But by issuing the command first, she got the important information out there as quickly as possible. Starting off with "Mooney on short final" or organizing her thoughts sufficiently to get his tail number out first (you can hear her stumble just a little on that even when she does give it a few seconds later) would have delayed at least a couple extra seconds before she got to the point of the emergency.
I think there's an argument to be made that she nailed it just right...
OK now, on-topic but perhaps off-task, a couple questions:
(1) Do controllers regularly check the undercarriage of landing aircraft? If so, is there any procedural mandate or guidance on this? I've always assumed that there is no promise whatsoever of any kind of visual check, and that any such advice given is completely optional and done only as workload permits. Can anybody confirm or clarify this?
(2) Hypothetical: I'm in the run up area or perhaps holding short. I see the Mooney coming over the numbers, descending through 50 feet, and his gear is up. If I'm not hearing anyone else on the tower frequency, my inclination is to key up and say something like what our controller said here: "Go around, go around, Mooney go around, your gear is up..." (And I might well lose control and yell or screech it out, not being as collected as a controller...
Holy crap, me, with my PPL, sitting in my dinky little 172, I just issued my first clearance. Am I right? Wrong? Is this a twisted extension of 14 CFR 91.3 (b), where I can deviate from any rule to meet an emergency, and explain myself later? Except in this case, it's not my
emergency; I'm not PIC of the emergency aircraft... I still think I'd key up and try to let him know.