Well maybe in your part of the country and OP's , its done that way but not here.
Between both my kids, they have been to at least 50 birthday parties and seriously I can't think of 1 that didn't serve food.
True the OP doesn't have to do anything she doesn't want to, she asked for opinions and I'm just saying at dinner time I would expect my kids to be served something more than popcorn or cake.
She doesn't have to serve anything for all that I care, I just gave an opinion and how things are usually done in these parts.
And certainly if the OP decides not to serve dinner food, it should definetly clearly be stated on the invitation.
Well, as someone who lives where the OP lives, I can assure you that the parents expect pizza - out of over 100 parties my kids have attended, I can only remember a couple that didn't serve pizza, and they were at odd hours.