Is it possible to be instant on/off? Yes. Is there a market large enough at support building such a machine currently? I would think no, people generally want

Is it possible to be instant on/off? Yes. Is there a market large enough at support building such a machine currently? I would think no, people generally want more than a typewriter with a screen. Early computers did turn on almost instantly but program load times from tape or disk was slow. Although in some instances I could say from direct experience that a c64 power on to text editor can be faster than a modern computer. I believe back in the 80's the was some single purpose computers built with word processing, spreadsheet and other very basic office programs built in. These would be very fast but might not meet your idea of an OS. Old systems that had cartridges, if you could find a text editor, also should be very fast. Again the idea of what you mean by OS may not be met.