Interesting idea. I do think limitations can in some paradoxical way inspire more creativity. For example consider guitars with one pickup like an Esquire compared to a Tele. A tele set to the bridge pickup doesn't provide the same experience as playing an Esquire. It changes how you as a player operate the guitar. You come to accept the limitations and do different things with the guitar. You end up picking differently or using other tools like the volume and tone controls. Or it just frees your mind to go elsewhere with your playing or music. In the same way removing all knobs from an amp could in an interesting way free you up to focus on playing in a different way. One question of clarification I would have is whether you would take an existing circuit and replace its pots with fixed resistors - or if you want to approach it from a design perspective about how one could make an optimal bare bones amp with no knobs. I find option #2 to be a little more interesting personally.