I taught myself with a mixture of books and Mum's support. So it can be done, but I think it would be useful for children to use this sort of thing in a subject like textiles, rather than stuff most will never use again.
My dad was a very good carpenter. Not his job, but he made from scratch (eg chunks of wood) a lot of the furniture and fittings at my parents' house. He learnt the basics at school, and discovered in that he enjoyed it and so did more.
I think looking at doing practical real life work that can be used in future would be far better than lots of theory. I'd do as well as the sewing:
Cooking: how to cook to live
Woodwork: Repairing and basic DIY
Budgeting and understanding saving: Part of the maths syllabus
And in year 10 and 11, one lesson a week to do basic practical things:
Check a car over, and do necessary basic maintenance, wire a plug, basic cleaning, garden maintenance, oil a hinge, baby care, basic plumbing, reading a map (yes, I know Satnavs are easier, but as a back up), first aid, putting up flat packed furniture, recognising dodgy statistics, recognising signs of depression in others and where to go to get help etc.
Lots of things that would be useful for people to know and I see an awful lot on my local FB group of people asking for help for this sort of thing.