I dreamed of a moment when further existence of the society without clear and non-ambiguous personal responsibility will be impossible.

This is that. In olden days, even if an apparatus made a decision, it still consisted of people. Now it's possible for the mechanism to not involve people. Despite making garbage decisions, that's something new, or, to be more precise, something forgotten too long ago - of the times of fortunetelling on birds' intestines and lambs' bones for strategic decisions. I suppose in those times such fortunetelling was a mechanism to make a decision random enough, thus avoiding dangerous predictability and traitors affecting decisions.

The problem with AI or "AI" is that it's not logically the same as that fortunetelling.

And also, about personal responsibility ... in ancient Greece (and Rome) unfortunate result of such decision-making was not blamed on gods, it was blamed on the leader - their lack of favor with gods, or maybe the fortuneteller - for failing to interpret gods' will, which, in case they could affect the result, correct. Or sometimes the whole unit, or the whole army, or the whole city-state. So the main trait of any human mechanism, for there to be a responsible party, was present.

Either a clearly predictable set of people in the company providing the program, or the operator, or the officer making decisions, or all of them, should be responsible when using an "AI" to at least match this old way.