I definitely think this would be a great idea. In many ways it could be implemented in the same way that Snapchat has Trophies. I also had a couple of ideas following on from this, @Andy71uk.
Trophy cabinets - See all of your achievements and badges
Obtaining certain trophies / hitting saving targets opens the opportunity to be entered into prize draws for merchandise (Mugs, t-shirts, hoodies)
I saw another page on the forum focussed around different card colours; this could be a way of implementing them?
I see this as more of a third party integration however, it would make a great addition to (potential) kids accounts in the long term future. Anything which would help children to learn more about saving would be a massive plus!
Perhaps not the social features but definitely the badging/achievements anyway!