Re: Innovation? We've heard of it
I'd bet if you wrote an OS for the phone in machine language customized to the exact CPU set & hardware in the unit & took out most of the GUI stuff and had your applications written in assembly with no extra linked libraries of stuff they don't need, you would see your phone work faster than you could imagine.
However, you'd have almost no apps as it's a bit hard to copy/paste your way to working programs in assembly or machine language.
There was an article a few years back about a company building some car sensors / displays based on a very stripped down & hardware customized version of Linux, getting sub second power on till fully working & accepting input / displaying results times.
Then for extra points you could always try for the compressed self relocating machine code type programming.