Swim teacher here.
I agree with you that the swim England pathway is purely about making money. 10m butterfly at the same time as 10m backstroke (stage 5) is insanity. No swim teacher will agree that that’s the best way to get kids swimming, so it can only be about making money.
so I’ve set up my own swim school. For distance and deep end. I run special classes where I don’t care if you have a screw kick on breaststroke and can’t get your fly arms over, I’m not going to limit you to 10m to correct those techniques, when you can get on with 400m backstroke.
that said, you spoke op that your dd isn’t breathing correctly in the water, which ties in completely with only 6m. That is fundamental. There is no value on working on her stamina (you can’t anyway if she isn’t breathing correctly) when she isn’t breathing right. The teacher is right to have her in the lowest group, that’s basics number 1.
also, you and others on this thread, are keen to direct blame somewhere - the teachers, the pool, Swim England pathway etc - when actually, none of you are saying ‘my dc is really really poor at learning to swim.’ But that is the crux of it. If others are moving quickly through the groups, then it isn’t the teaching, nor the space, it’s your child.
and to conform to quite a few posters upthread who have confidently claimed ‘you can’t teach a child to swim in 12 school lessons’. I can. If the child is able to take instructions without fear. I’ve done it plenty of times, get very excited about taking a non swimmer in September and getting them kick a length on their back by December. It’s my favourite bit of my job!
And one final thing op - why would you complain about your dd being in the lowest group when she was stage 3, when you had absolutely no idea of the other children’s standard? It is entirely possible that stage 3 at 9 years old would be the weakest swimmer in the class. General rule where I live (an affluent area), but stage 1/2 - 5yo, stage 3 -6yo, stage 4 -7yo, stage 5 - anything from a 6yo up to 10yo. Club swimmers start sometimes from 7yo. So they’re doing 2km in an hour.