and at all the misunderstandings of the social side of HE!
OP: Not learning what you think ought to be learnt in school, policies etc. are not the only reasons to HE. Try to see it as a positive, proactive decision, rather than a negative, reactive one. You talk as if you need to have a very good reason to HE, like something really awful happening at school, but lots of HEors choose not to go the school route because they think the school system itself is good enough reason!
HEing doesn't have to be expensive. Local HE meetings are usually not expensive at all - we go to three different meets through the month, two that meet twice a month. These all cost £3 per family.
We go to a free PE club that a local HEor runs - he has a free venue (payment for HE things is often just for venue and materials because lots of HE parents run things to skill-share). We go to a choir run by a local musician HEor - £3 per family again.
We go to friend's houses. All in all, we meet up with the same set of HEing families, in different combinations and all together about 3 or 4 times per week!
Children do not need to meet with the same 29 children every single day to learn how to live in the world. All the HEKs I know are articulate, happy, sociable, mature children. They do not need school to make them so! They also usually do not spend all their time just with their parents, contrary to popular belief!
I disagree with what Orm says (DH and I think of school as the place where they teach the things that children have to learn. Home is where they learn the extras. ). Children learn the things they have to learn by living. For example, they learn all the maths they'll need through being involved in shopping, cooking, planning, counting and spending pocket money, calculating how long journeys will take.........when they want and need to know more, they'll be motivated to find ways of doing it - using an online programme like Education City, finding a maths tutor, buying maths books......
I say YA totally NBU and would be making a very positive and progressive decision.
BUT do see what your DD wants. I agree that she's too young to really understand, but it might make her very unhappy if she's settled in school now and is enjoying it day to day.