I was thinking about Bad Apps that users voluntarily hand their login details to (so they can download snapchats they get sent). Those don't need root, since they're just mimicking the Snapchat app and receiving the photos directly.

But it doesn't work, since you need some way to generate new API keys for your second device... which could be a Bad App.

If you 1) enforce one key at at time (so one "device" at a time), 2) rate-limit key changes (if you switch to a new device, or Bad App, you can't switch back within a day or two) and 3) eliminate Bad Apps in the app stores- you effectively limit Bad Apps to being entirely web-based, and hopefully the restrictions on webapps will make the Bad App sufficiently a pain in the ass to use that people won't want to switch to it, even though it lets them save photos, since it locks them out of the real app.