The hardware has state that is exposed more or less directly, but texture management is all just plumbing and easily wrapped. Most of my experience is with directX though, which seems to have a much cleaner API.
Anyways, immediate mode UIs abound for game stacks given the ease at which they can be mapped to the GPU directly.
DirectX still uses stuff like ID3D11DeviceContext::PSSetShaderResources to set application-global state that's required to do anything. It is fundamentally stateful and non-pure. I'm not sure why you're trying to argue this point.
Anyways, immediate mode UIs abound for game stacks given the ease at which they can be mapped to the GPU directly.