If hypothetically they were supposed to be responsible for returning the cans, they'd quickly discover that they don't have access to many cans, and that they have absolutely no way of transporting them to a recycling center, or even going to a recycling center without bringing any cans.
My sister visited me over the summer a couple years ago, when she was 8, and I let her hold on to the jiao I received as change (US equivalent value: roughly 1.5 cents to the jiao). This made her happy (especially when she noticed a chinese mother doing the same with her child), but I didn't think it was some big project to teach a child about money; I did it because it made her happy and the quantity of money was too trivial for me to worry about her screwing up. It was trivial for her too; she never saved up enough to buy anything (most likely candidate: a roll of mentos, which would have cost 20 jiao. Turns out it's kind of inconvenient to carry around dozens of tiny coins.).
Anyway, as far as I can see, pretty much the only initiative a child can show is to pester their parents into recycling the cans for them. That doesn't differ much, in my mind, from just pestering the parents into giving them money.