Sure, but democracy is the ruling of the people.

Will a vast intelligence that gets smarter exponentially every second agree to subjugate itself to the majority even when it disagrees? Why would it do such a thing when it is vastly superior? Will it not develop its own interests completely alien to humanity, when it's cognitive abilities far surpass anything possible by biological systems alone?

I think democracy is out the window with the advent of AGI. By definition we cannot make it value. It will grow smarter than all humans combined. Will it not be able to understand what it wants when it is a generalized and not specialized intelligence? That's the entire point of AGI vs the kind we are now building. AGI by definition can make those choices, can reprogram itself, can decide what is best for itself. If it's interests don't align with those of humans, humans are done for.