Leaving aside the thorny (and upsetting) issue of child protection, and back to whether there should be some compulsory check to ensure children are recieving an appropriate education...
I am not (yet) a mother. I do have an interest in education though. One of the many reasons why I would consider home-schooling, is because of my educational philosophy.
I believe that the school system of memorising in order to regurgiate answers in exams to earn grades is damaging and counter-productive. It expects all students to develop at the same rate as those born within a twelve month period. It demoralises those who need extra time to grasp a concept by labelling them a failure, and it limits the potential of those who are enthused by a subject by telling them they've learnt everything they need to about that topic. It stiffles creativity and problem solving by making children fear humiliation by saying the wrong answer aloud. It encourages children to be competitive (top of the class) rather than co-operative (learning and assisting their peers so the whole class learns).
Awarding grades (for every subject, rather than for qualifications that a teenager decides they want for themselves) damages their intrinsic motivation to learn, their ability to critically evaluate and improve their own performance and their enthusiasm for the subjects involved.
And that's before we get to exam related stress and depression.
A compulsory test or exam to show off my children's abilities would be counter to that educational philosophy. I'm not saying there could be no way around this, a child might be willing to share project work, or workbooks, or the testimony of a music tutor to prove that they are indeed learning. But schools have parent-teacher evenings and report cards to demonstrate to parents that their children are learning because the parent doesn't see what goes on in the classroom. Home educating parents can already see that their children are learning, and want to maximise their wellbeing and development, not compare them against other people's children.
I think it's important to realise there are many reasons to home school, and compulsory testing may well be one reason why parents and children make that choice. The last thing they want is to have a compulsory test for home-schoolers (and it's not because they have something to hide).
If my future children do end up going to school, I know I'll have to help them see past the grade culture and encourage them into a philosophy of life-long self-motivated learning. I'd rather they never found out that writing could be boring (as those made to copy out loads of sentences only to add capital letters to them in schools will remember) that they just saw it as a way of communicating and expressing their ideas across time and space to other people. I 'got' that sentences and proper nouns needed capital letters from reading and writing normal sentences, I didn't need a special exercise with dozens of examples just to keep me quiet whilst the teacher listened to another child. Where as maybe other kids did need that repetition, but it would've been nice to have been treated as an individual.
Most parents choose to home educate because they have a huge interest in their child's education and emotional development. It is a huge insult to them to be singled out as likely to fail their children, when schools fail thousands of children every year and are still seen as the proper choice. Testing skews learning to pass the test instead of following what is appropriate, interesting and challenging to an individal child.
For a reasonable idea of my views on education at the moment, watch any Sir Ken Robinson TED video online, and read Alfie Kohn's 'Punished by Rewards'.