There's quite a lot to address there. You're obviously disappointed on your DD's behalf, which we can all understand and empathise with - you'll find the parents on this thread all know how brutal the performing arts can be, and are very supportive when things don't turn out as hoped.
However, if you choose to view the offer of a skills course as a wooden spoon, that's your prerogative, but as a 'veteran' parent of a performer who has had many successes and just as many rejections, I would caution against allowing your daughter to pick up on that attitude. Something that is highly valued and nurtured at NYMT (and in fact in the industry) is humility and respect for other performers. There may be other parents on this thread whose DC have accepted skills courses; talented DC, who for a multitude of reasons may not have secured a recall this year. The skills courses always get great feedback - hopefully a previous participant will come along and attest to this - they have fantastic creatives leading them and the DC almost always feel they have made lots of progress.
There's no reason to suspect the NYMT courses are less good than anything offered by the vocational schools, which any parent who needs childcare can dump their DC in for a week in the holidays regardless of whether the DC have any interest or aptitude! The DC on the NYMT courses bothered to audition, and had the courage and commitment to learn a song and perform it in public, so I'd be inclined to think they are serious about wanting to perform.
In no way would your DD be viewed as having 'failed' an audition. Everyone there would be in the same position, and sometimes DC get noticed at skills courses, helped with whatever may be holding them back, encouraged to audition again, and then the next year the outcome is a show.
Not getting recalled doesn't mean anybody is saying your DD isn't talented. From everything she's done it sounds like she is. But NYMT is auditioning all over the UK - lots of applicants will be the best singer in their school, or the lead in their local show, but the standard is high and they may be in a room with 20 other DC who are the stars of their local youth group. Possibly she just didn't quite sell herself on the day, or as you say, suffered a loss of confidence. With over 1000 DC auditioning, with the best will in the world, NYMT cannot offer individual feedback. If they did it for one child, they would then have to do it for everyone - can you imagine how long that would take them? They are a very small team. They look carefully at the scores and comments in each skill from the creatives on audition day to decide what the best offer for each individual is. Of course it's possible that occasionally they don't spot someone's potential. I have known very talented young people not get recalls from NYMT and also not get offers from BYMT. That is tough for those DC, but it's also part of life as a performer. If they are really passionate and committed they will find the resilience to come back and show their true talent the following year.
One last misconception to put to bed. NYMT may decide that someone is not right for this year's shows based on one of many reasons - it's not for me to attempt to know what they might be - but I want to say unequivocally that body shape would not be a factor. In my ten years as an NYMT parent I have seen DC of all shapes and sizes cast, and NYMT is refreshingly different from the West End audition processes where children get eliminated for being 2cm too tall, or not waiflike.
I'm glad you don't regret the day. Hopefully your DD enjoyed it even if she is sad about the outcome. Of course you don't have to accept the skills course offer, and if a mistake has been made and your DD's talent has not been seen, I can only encourage you to try again next year. They do notice repeat applicants.
Wishing your DD all the best for her BYMT audition. I hope she has a great time and nails it.