Is syscall a public API on iOS? In the end, you have to call that to get anything on the screen?

Looking at unistd.h, it seems marked as

  __OS_AVAILABILITY_MSG(ios,deprecated=10.0,"syscall(2) is unsupported; "
    "please switch to a supported interface. For SYS_kdebug_trace use kdebug_signpost().")

and syscall numbers seem wrapped by

  #ifdef __APPLE_API_PRIVATE

in *<sys/syscall.h>

Not at all, it is a Linux thing to keep applications doing syscalls, like back in MS-DOS interrupt days.

All other modern OSes give zero guarantees about syscalls.

Indeed, you have to call UI Kit, that is the public API for userspace applications.

Even if via OpenGL ES or Metal, you need a drawing context and a Window to render it.

Everything I described is in a public header right inside your iOS SDK folder

I doubt you can render an UI in pure Assembly and show it on the screen without going through UI Kit in a non-rooted device, given that even the device drivers extension points is quite limited.

Which was the whole discussion point that started the thread, how to make a iOS app with zero references to UI Kit.

This isn't an 8 and 16 bit home computers, or games console, with an address for the framebuffer.