I don't recognise the description of "learning just 3 pieces a year" either. I didn't do exams until the very upper years, but did follow a similar program, but I certainly did many pieces, not just the exam ones. My teacher also had us choose a book of music if we wanted like pop songs, show tunes, Xmas carols, etc, to do in addition to classical music.
The assumption that children should want to play with each other, jam, compose, express etc, sounds a bit anti-classical-music to me. All those are great skills if that's what a child wants, but who's to say that they should be what music is about, any more than learning classical style? I'd have been so turned off music if I'd have had to do that. I was very shy, very unexpressive outwardly, and hated any sort of improvisation stuff. Yes, I wish there were aspects of it that I were better at, but certainly lessons like that would have put me off and I'd have quit early on. Structured, formal lessons suited me. I didn't want to do exams, and that was fine, but I still learned the technical requirements, a large selection of pieces, etc. Lots of effort was put into technique like bow hold and sound quality too - and as far as I know, that certainly does matter for exams! - but the point wasn't to learn it for passing exams, but to have a nice sound. I played in many orchestras and loved being part of a bigger group that my little sound could contribute to.
I didn't particularly find scales or exercises fun. There were lots of times that I didn't want to practise. But I'm very glad I persisted and was encouraged to. If things aren't fun, it doesn't mean that the child isn't getting a lot out of it still - much of it depends on the child's personality. I don't think I'd have found some of the methods described here fun at all either. The entire experience was enjoyable for me, particularly being able to be part of orchestras and bond with a group that way, but it doesn't mean I enjoyed every aspect of it.
I do wish I'd done more exams on violin as well as piano, because I can see now just how much use the technical requirements would be in further playing. All the arpeggios and scales and so on that seemed boring to me at the time, and that I didn't practise much because I didn't do the exams, would come in very helpful now for orchestra music. But I preferred to concentrate on pieces. I played things I liked. I played duets with my teacher. But I didn't do some of the things I found boring, whereas I did on the piano because I did them for exams, or at least, following an exam-style progression, whether or not I did each individual exam (I did some but not all). I generally enjoyed working for exams. My stage-fright let me down in terms of actually doing them, but I enjoyed the structure and method of them.
I had good teachers, for piano particularly, who were by no means exam focuses, even if they did do exams with children. Exams themsevles aren't the problem, but poor teaching is.
So I think it really depends on what a child's personality is like, and their musical goals. Some of us wanted a classical music education. Doesn't mean it's for everyone, but it doesn't mean that there is anything wrong with it, either. So we can't do some of the skills that you think are important - I doubt I'd have been able to do them anyway, and why should my interests and talents have been ignored? I'd have been a nothing in your sort of system, wouldn't have shown any talent, would have been unhappy with lessons, and wouldn't have ended up doing anything musical. I wanted to learn to play in an orchestra, to play classical music. There's room for lots of different approaches and skill sets.