I haven't been faced with this yet, as my eldest is only in Reception (it's his birthday tomorrow and he's happy to go in, so different for us).
I wouldn't say never though. It's one day, you know your child, and your home circumstances. Of course education is important, and children need good educational attendance (be that regular home schooling or regular attendance at school), but we must remember the mental health effects on children. I think expectations of children are often too high. Yes they need to do things they don't like, yes they ahve to learn to be resiliant as they won't cope with life in general. That being said, I still can't see how having ONE day off for their birthday will have a significant negative impact on those things, but I can easily see how it could have a positive impact on their self worth and mental health.
They'll feel listened to, and that their needs and opinions are respected. As long as it's made clear it's a one off for their birthday, and that they can't opt out every time things get hard, I really can't see how it's going to cause any lasting issues.
(I was a teacher before I had DS, and now work tutoring within the home education community for context.)