If my kids want to give their sibling a birthday gift, then fine. No biggie.
So what if it is me who is paying for it.
It is the thought of it.
That they love their sibling etc.
But for my kids, I don't make them do this, nor tell them to do it. BUT often, them giving the other sibling a gift means... they make something for that sibling. And it is all THEIR own idea. I don't even tell them "make something for your sister/brother..." they come up with it on their own. They want to.
And even if it is a bought gift from a store... THEY choose the gift for their sibling. And I buy it. And in that case, my kids know fully, what a "budget" means. My kids are 6 and 10.
Or, sometimes they will use their own money. And again, this is THEIR idea. I don't force them to use their savings. They, want to.
Sure my kids exchange gifts. Why not?
My kids don't get an allowance either. But they have money they earn from doing various things or money they got as gifts or the tooth fairy etc.
I don't MAKE my kids, RESPONSIBLE for gifting their "family."
Because, things like this are just tradition or it comes from their own wanting to, their own heart.
It is not a "chore" to them, not a hated responsibility.
As a Mom, I see myself, as being "responsible" for remembering occasions and gifts, ahead of time, and getting it. I don't expect my kids, to do that. They don't drive.
And I certainly don't expect them to be responsible for gifting the entire family.... me/husband/siblings/grandma/aunties or uncles etc. etc. etc. plus, their friends. We do it, as a FAMILY. It is a family, activity.
I don't make... my kids, exchange gifts for their birthdays or Christmas. It comes from their own volition. And the responsibility of who pays, is not rigid.
Then for my kids' friends, they choose the gift, we have a budget of which my kids know what that means, and we go to the store together, they choose a gift that THEY choose, and I buy it.
No problem.
Your son is 6, he wants to get his 3 year old sister a birthday gift. Whether he makes somethings or he picks it out and you buy it, I don't see a problem with that. He is 6.