Now that (as of last week) you can get a certificate to compile apps for your device from Xcode for free, it's totally possible. Someone would have to write an app that bundles an IDE, clang, codesign, etc. Fetching that certificate could be done directly by the app or through a proxy; this is the only sticky part, because I'm not sure whether Apple would approve an App Store app that uses undocumented web service or Xcode to do so, but the thing is, if Apple doesn't like it, there is now the "nuclear option" of staying off the App Store and having a web service that fetches said certificate, signs the IDE itself with it, and sends it to you. And it may not be necessary to go that far, perhaps depending on how much is being done on the client side versus the server.

If you add a Bluetooth keyboard and a TV, an iPhone starts to seem like a totally reasonable development platform...

Edit: By the way, if HTML dev (including local) suits one's needs, which for a beginning programmer it well might, that's been possible for a while. C.f. "Procoding".