This is a feudal view on things.  Normally, people are not "subjects" but are in principle free.  They should be free to work together and organize them into bigger structures (like "states") if they want to, on their own free choice.  States should be subject to people, and people shouldn't be subject to states.  I know that this is not how things worked out the last 5 millennia or so, but that is exactly why states are thugs, submitting people to their will by using their violence.  As I said before, it is not because things are different than what they could be, that we should necessarily cheer for the way they are now.

Indirect democracy didn't submit states to the people, that is just a pipe dream.  It did improve a bit the situation over the established absolute monarchy, but not much.  We can only change the absolute monarchy every few years.  That did bring some softening, but didn't solve the fundamental problem you pointed out: that people are still subject to states instead of the other way around.