Wow, I would fight a school policy like that. Fair enough request being subtle about giving out invites (give to teacher or direct to parents etc), but I don't think any school has the right to say who should be invited. I get where they are coming from, but a policy???

I have found as they get older they tend to want sleepovers, so the numbers are quite low for that (2-3 friends), so it is less of an issue and the kids seems to be so much more understanding.