Children need to be feed and not just cake and sweets, there is no point in the day where a parent won't have made allowance for your party and their children's meals.
I would be livid if I took my children to a party and they didn't get some sort of meal..and I would expect it to be crap btw, nuggets and chips et al, rare to get food I would want to pick at, so no, if there is opportunity for the parents to buy their own food and drink without disappearing then don't feed them, this is not unreasonable, if you are going to a park, and the parents can't get food and drink then massively unreasonable.
if it is such a massive pain why are you doing it? my twins have only had 2 Birthday parties, 1 at 1 which was to be fair was a house warming as well and their last at 8, a three year old will not remember a party.
but my top tip on party food if you are going to a spot? order Pizza, I went to a Children's party in the USA when I lived there which is why my boys had no parties as I could not get with the etiquette and the Mum was even more out of her depth than me as she was Japanese, she ordered a tray cake....they are massive! I too would have made that mistake if she hadn't done it for me..
but the pizza's where ace she ordered Lots of just cheese about 4?, 2 pepperoni, 2 ham and pineapple, 2 veggie. 30 children and accompanying parents
for 10 children, order the biggest size and 2 just cheese, 1 pepperoni, 2 veggie, I bet that is enough for the parents to have a pick at and satisfy the children.
and if you order in advance they may do a 3 for 2 deal if you ask nicely :0)