Hmm. Honestly, it just feels to me like this is asking the question backwards. Whenever you state that you can create mobile device X to serve purpose Y using an OS based on AOSP, I get the feeling that I could already point to an existing mobile device X serving purpose Y that runs Google Play-based Android. Or, at the very least, I could produce such a device. And in doing so, I'd avoid all the costs of creating a new OS, and still be able to sell to users who already have experience (and infrastructure!) running standard Android devices.

If, instead, what you are trying to sell is the OS itself, I think you need to look at the concept of the OS in a new way. The Solu guys are a good example here; they are (bizarrely in my opinion) still tying themselves to a specific hardware device, but their OS is instead mostly cloud-based, and allows you to perform tasks that straddle devices (and the internet itself). In short, they do something that iOS and Android don't do (or, at least, don't do well).

You can't just have a reason why the user would want to use your OS; you've gotta have a reason why the user would use your OS instead of iOS or Android. I don't think you can beat them on usability alone; they are both quite usable for the average consumer. You've gotta have a different argument -- run on older / smaller / stranger hardware than they do, work in ways they cannot, perform tasks they cannot. The privacy argument is good, but privacy isn't a task; there has to be something concrete that the user can do with the device that will cause them to feel the need to purchase it.

Anyway, apologies for the long rants here.

tl;dr: Competing directly OS-to-OS with iOS/Android ain't gonna work. Better to first build up an infrastructure where iOS/Android aren't competing, before trying to go mano-a-mano with them.