So you want to reduce the quality of the party. Unless you’re buying fifty-cent bags of Doritos, you’re always going to reach a point where you’re overspending because of too many guests. There’s other issues to the size of a guest list than the cost of refreshments. There are space issues, for instance. More guests means more cleanup, for instance. More kids at a party–and twelve-year-olds are kids–means more potential for raucous behavior.
Twelve guests for a twelve-year-old seems quite adequate. It means restricting the guest list to the kid’s actual friends.
I do think, for better or worse, that written thank-you notes are considered rather antiquated these days, apart from very formal occasions like weddings and graduations. I don’t have kids, so I don’t have to decide issues like those described in the OP.
Having been brought up by somewhat traditional parents, I was taught to write thank-you notes as well. When I was young and first out on my own, I often did write thank-you notes after things like birthday parties, informal get-togethers, etc. While nobody was exactly upset to receive them, it was clear from people’s reactions that they hadn’t expected them, weren’t quite sure how to respond to them, and considered me a bit of an oddball for sending them.