Yes, I do think that the line "it's my child's intellectual property and she hasn't agreed for it to be shared" is overused. It's technically true, but except in cases where the child feels very strongly, it's beside the point. After all, my teen also has the right to refuse dental treatment, but if she did, I'd exercise my powers of persuasion on her and try to talk her round. There are much better reasons not to supply samples of the child's work to the LA. I'll list some of them.
It's misguided and unhelpful of the LA to ask for samples of a child's work, because that doesn't help them to carry out their statutory duty to intervene if a child is not receiving a suitable education. The child's "performance" is not indicative of whether she's reciving a good education. By the same token, supplying samples of work doesn't help you to demonstrate the suitability of your provision. You are required to provide an education suitable to the child's age, ability, and any special needs they may have. Since the LA doesn't know your child, supplying a piece of "work" can't tell them whether you are doing this.
Forgive me one of my possibly dodgy analogies. Suppose you were assessing the competence of a vet who had treated a racehorse. The question of whether that horse later won a race tells you nothing about whether the vet is any good. The worst vet in the world might happen to have worked with a perfectly healthy horse which went on to win the race. On the other hand, a very capable vet might be unable to cure an ill horse and make it capable of winning the race. If I were the owner of that horse and I was deciding whether to stop using that vet, I wouldn't be asking whether my horse had won a race. I'd be asking the vet, "Do you think anything is wrong with the horse? Why do you think that? What treatment did you give? How can you tell whether it's working?" Ultimately, I'd listen to them and decide whether to trust that they seem to know what they're doing. Probably I'd assume they were getting it right, unless they come across as a total quack.
Because the LA doesn't know the child like the parents do, when you describe what the child wants and needs, at the end of the day they're going to have to take your word for it. When you write a report outlining how you are meeting your child's individual needs, they have to decide whether you appear to be a complete charlatan. If so, they must take action.
An LA which asks for samples of work is an LA which misunderstands the law and the nature of home education. They're attempting to assess the child's performance rather than the education.
So, providing samples of "work" is unnecessary. But is it harmful?
Some children react very strongly against having their learning judged, and may find it stressful. Some may fear that if their arithmetic isn't up to scratch they will be sent to school. Some kids don't actually produce physical output when they learn. If many parents supply samples of work, LAs then say to the few who don't: everyone else does this, so you have to as well. I don't think it's a great idea to encourage the LA to bark up the wrong tree like this.