The vast majority of people who are currently using bitcoin did not have someone else secretly backing up their keys or seed phrases for them, and yet here we all are. I think it's far more valuable to sit down with someone and teach them proper security practices than it is to treat them like a child and secretly perform the security for them. I think doing so would lead to carelessness down the line as you are teaching them there is a safety net (you) which won't always be there.
This is different, people who came to Bitcoin on their own are much more motivated about the proper use of it. But when you gift someone Bitcoin, especially a small amount, they'll likely just put it in a drawer and forget about it, and then years later, when the price increases by x10, they can no longer find it, which will likely cause them to never want to be involved with Bitcoin again. This is the scenario that I kept in mind when I suggested to keep the copy. But if the person who receives the gift shows a lot of enthusiasm, they can indeed be encouraged to move the coins or use their own wallet from the start.
. 
. 
