I don't know if this is popular in the USA. We also have a "no gifts" rule. Instead we do a secret santa. We do a real gift and an optional gag gift. It works wonderfully.
Except this year somebody sent lots of gifts for two of my nephews. It was ridiculous and very uncomfortable for the rest of the family to watch.
Gift-giving can become such a social minefield too. We had a birthday party for my oldest son and specifically requested no gifts (he has enough toys). One attendant missed it or ignored it and brought one anyway. We politely thanked them for the gift, and were immediately confronted by several other parents who became quite defensive and a little angry with us (seemingly embarrassed that they had not brought gifts). Some of them even came back after the party with gifts to somehow make amends in their minds. There's a lot of social stuff I don't understand surrounding gift-giving.