Reminds me of writing Win32 applications in C + Asm, although it looks even more difficult because the documentation is lacking and there's more stuff that has to be done. I find the fact that a simple, "do nothing" native iOS app is much bigger than some very featureful apps on other platforms somewhat sad... I don't know of any 64k/4k demos on iOS either.

Great work for trying it though. Are all those bytes actually needed? E.g. I see a lot of "restore VFP/Advanced SIMD registers" when you don't seem to be using those at all. It would be interesting to see how much you can cut out, as currently it looks more like a mostly mechanical ObjC -> C -> Asm translation, like a compiler would do, instead of a human. As a point of reference, on Win32 an app that just shows a window with some text in it requires <1KB of binary.