It seems like it would be super useful if an app existed for iPhone/Android that emulated a Bluetooth keyboard or mouse. e.g., you turn on the app, and suddenly you can type on your iPhone keyboard and your PC/PS3/etc. pairs with it as if it were a Bluetooth keyboard and receives the typed letters.
This idea seems so intuitive to me that I am thinking the only reason it doesn't exist is that it is not possible, but I don't understand why it wouldn't be possible.
Is there a limitation of Bluetooth which prevents a device from emulating a different type of device? Or, perhaps, a limitation in the APIs exposed by iOS or Android which would inhibit this?
EDIT: it looks like the iPhone Bluetooth APIs are fairly limited as you can only communicate with Apple-licensed accessories: Is it possible to develop an iOS app with bluetooth capabilities? This would presumably rule out anything along the lines of emulation of another type of device. The question is still open for Android though.