L.C.
We had the opposite problem at our kids' parties: parents expecting 2+ hours of free babysitting in exchange for a gift. Since I wasn't interested in hosting a party and running a daycare simultaneously, we always put 'please bring a parent' on the invites.'
I always appreciated the kids having their own people to work through any anxiety or upset with, leaving me to just deal with my kids and the party stuff.
We were heretics, though. We had a rule that the kids could only invite the number that they were turning --so if they were turning 9, they could invite 9. We never invited a whole class of anyone, mostly because our kids had friends from so many different places (girl guides, gymnastics class, dance class, acting classes, family friends, etc) that they had to be really selective. I always wanted my kids to know that their events (and their home) were 'theirs' so they had every right to invite (or not) the people they wanted (or didn't want) to host.
We never fed people --we timed the parties for after lunch and well before dinner, and indicated on the invite that there would be cake and ice cream, with tea and coffee for parents. We always had enough cake for parents, too, but didn't advertise it. Mostly, the food rules came from knowing so many people with restricted diets (celiacs, vegans, vegetarians, allergies, etc.) and the range of 'picky kid' eaters, that it wasn't enough fun for us to try to accommodate everyone.
Because we didn't invite whole classes of people we barely knew, the girls often invited all the kids from a family in the first place, so unexpected siblings never came up.
I actually can't really imagine not being incredibly rude to someone who appeared at a party uninvited and then expected to be 'included' --particularly to the parent who started it. Can you imagine doing that? 'Hi, I found out you were having a party, do you have a costume for me?' Sheesh.