I really don't see what the issue is. I don't want to be spending money on something that I think a child will like, only for the child to never use/play with it. What a waste of money. So an Amazon wishlist seems like an excellent idea. Presumably there will be a large range of items to choose from, so you can pick something according to your budget.
And it's not like its the the ONLY things you are allowed to buy. If you knit/sew/craft something you know the child will like, then there's no problem. You're not forced to follow the wish list.
And at three years old, the child wouldn't have a ruddy clue what parents put on Facebook, or even what an Amazon wishlist IS, so it's not "teaching the child to be greedy" or rude.
Is an Amazon wishlist any different from asking a parent what the child wants - or having a wedding list? No one slates a bride/bridegroom for having a wedding list at a shop, do they? This is just the online equivalent.