In the long run, it is highly likely that you will either be an ancestor of every single human, or none of them. (http://www.bbc.co.uk/news/magazine-19331938) You don't need to give every single one of your descendants a gift. Give 2-5 gifts a year, randomized after filtering out undesirables using a naughty/nice algorithm.
Assuming total population remains roughly the same, if enough people did this, it would actually work. Most kids would get gifts from grand^n Santa.
Nice idea and an interesting article. If the goal is to be remembered for as long as possible giving more presents is obviously better. After 9 generations only a small part
But some might feel that a enormous list of children with ratings of their behavior would be questionable.
Assuming total population remains roughly the same, if enough people did this, it would actually work. Most kids would get gifts from grand^n Santa.