Everyone gets one childhood. I wanted my kids to have fun. The Santa/Easter Bunny/Tooth Fairy traditions are merely fun games of anonymous gift-giving.
I think you have hit on a good reason not to tell kids Santa isn’t real. The word “anonymous.”
The kids don’t have to feel grateful to their parents for all the gifts. That would kind of spoil things a little.
But I can see doing it the other way too.