I think I'm going to incorporate this into my own personal Santa theory. There is only one Santa: Santa Claus, LLC.
All the Santas we see are simply part of a network of Santas. It's how all the kids who visit Santa can get their Christmas wishes relayed to the home base in the North Pole. There are plain clothes Santas, too, monitoring the behavior of people everywhere to determine who has been naughty and who has been nice. And on Christmas Eve, the Santa that NATO tracks isn't delivering presents. He's the Global Supervisor, or maybe VP of the Global Delivery Division at Santa Claus, LLC. He's coordinating the Santas who are working at the country level that coordinate the ones at the state level, and so on. All the way down to neighborhoods. They're like the postal service but they have a better attitude and a lot more funding in the form of Christmas magic, which, as OP said, they extract from those who still believe. It's not like they can just send out bills; they'd expose the whole operation that way.
Santa Claus, LLC is the biggest corporation on Earth, but nobody knows it because they're so well organized, and their logistics and marketing are contracted to literally millions of firms and individuals. It allows them to hear Christmas wishes, arrange gift creation/construction, and confirm delivery.
And home security firms are in on it; it's how your local Santa can pick your door lock without an alarm going off. And of course governments are in on it, because Santa Claus, LLC cooperates with them to deliver vital intelligence of naughty or nice nature. Governments are the ones who plant the memory into parents' heads that they were the ones who put presents under the tree. Probably radio waves or magic lasers developed by Santa Claus, LLC and delivered via wireless devices or something similar.
I've been thinking about this for a while now. The only thing missing was how they funded the whole operation. Thanks, OP. You figured out how Santa Claus, LLC keeps the Christmas lights on.