I've always done quite big parties for my kids. Things like soft play area, rent a hall and a bouncy castle, laser quest, go karting. And we do bloody good party bags with sweets and plastic tat and a book (cos I iz a well middle class mummy) and Something Noisy in. I particularly enjoy scavenging for bargains to put in them, and especially rummaging through the books in the Works etc to find ones that suit the kids who are coming.
And I'm really glad that I have done it that way. My Aspie teen still socialises with several of the kids that have been coming to his parties since he was two, despite the fact that he doesn't go to school with any of them any more and has never gone to school with one of 'em. I gave him a choice years ago of a big present and no big party, or a big party and no big present. He preferred to share the good fortune, and I'm OK with that. I'd rather spend money on doing stuff than having stuff.
We once no showed because I only found the invite, crumpled at the bottom of the bag, after the party. We've had a couple of no shows - I've generally been able to freecycle their place at the party to an accompanying sibling or similar.
Whilst it is a bit rude to not say if you have to cancel, I think the sender of the invoice sounds like a right pillock.