I think some kind of thank you is necessary. I remember how I hated sending thank you notes when I was a child. It seemed a huge chore. But nowadays there are easier ways to communicate. And if the child won't do it, perhaps the parent could?
Personally I'm done with "special occasion" gifts of any kind, both giving and receiving. Except for gifts to small children.
Sometimes I give an anonymous gift. For example, I left a baby gift for an expectant mother at her place of work.
For those who are worried about hard feelings if they stop sending gifts, why not say, "I'm donating to [name of organization] instead." Or volunteering, or taking a trip, or whatever.
I think that nowadays, most people can buy what they want, and/or the thing you give them will be the wrong kind. It's not like my mother's day, when she was happy to receive an orange for Christmas. An orange!