Growing up, I never got Christmas gifts under the tree from my parents. They all came from Santa (or relatives, etc). When I wondered about this aloud to them, I remember my mom saying that parents handle the gifts for birthdays and Santa gets Christmas! This is what we do now with our kids, too.
We don't do much for Christmas unless we're with relatives who celebrate, and then it's just a simple gift exchange. My 3 yr old doesnt know who Santa is yet, but will probably figure it out this year.
...Also, my in-laws have a nice tradition of everyone giving/receiving one secret Santa gift accompanied by a poem about the gift or the receiver. Everyone takes turns reading the poem aloud and opening their one present. I like how everyone gets their moment in the spotlight & its not just about opening a ton of gifts. Kids get more presents in addition to their secret Santa gift, but I've never felt the focus was on the gifts.
We are usually traveling for Christmas so when my oldest was a baby we started exchanging gifts to/from each other (Mom, Dad, siblings) the night before we’d leave. We have continued this tradition so my kids get gifts from family and from Santa. Last year I started the “Something you want. Something you need. Something to wear. Something to read” gifts from us and it seemed to be a big hit! Going to continue this from now on.
I do also one special gift from Santa for each, or sometimes together, and then for whatever reason, they have always assumed their stocking stuffers are from Santa too. Their Elf on the Shelf gives them a gift as does their two favorite stuffed animals and the rest are from me.