Why would you have to re-write your app from scratch? I'm assuming most of your actual business logic is in the Lambda code and the data model. Lambda wraps things pretty tight anyway, so just write a shim layer, and lift-shift your code to a new platform.
Completely agree with this. There is one project[1] we're working on which aims to provide said shim, but it's still early days. Developer tools will emerge to solve the major issues around serverless.
The difference is one doesn't have access to Lambda infrastructure itself. IF I write an entire app in XYZ lang, I can still run it on my own server or make it an executable and call the code through RPC. If I base all my work on a third party vendor infrastructure I can't replicate it requires an even more massive effort to migrate to something else, because now I basically have to re-write my app from scratch. FAAS may have killed BAAS but isn't going to kill PAAS.