I don't have an iPhone, but on Android there is the "Paperless Mobile" app (https://github.com/astubenbord/paperless-mobile), which can be used to scan as well. There are just some documents that I would prefer to have in proper and consistent "document scanner"-quality; I am always having a hard time with lighting using those phone scanners (although Paperless Mobile is one of the better ones I have used).
Those still have the speed disadvantage of a phone camera and need more space than a compact document scanner, I'd imagine. I guess a ring light for my phone would be an improvement; using the builtin flash usually leads to very uneven lighting in the scan.
