Hey can you drop this whole "responsibility" angle? I think it's an emotionally-laden approach that's quite unnecessary.
If you can explain why believing dungeon mastery is an important responsibility is an emotionally charged position, I'm willing to at least listen and consider backing off it, but at the moment I'm not understanding you.
To me, the Oracle is nice because it's a collaborative tool that creates a truth instantly agreed upon by both players and the DM. It removes a negative process that I've seen both running D&D and playing it: a DM who is making world-building choices in a stressful moment that either reduce player fun or aren't consistent with what has been established so far.
Sure, and if you or your players don't find that fun, you should dodge it, but
own the reason. Use a random generator because it is more fun, not because it solves problems that dungeon master fiat doesn't, or because it keeps players from blaming you for bad outcomes. Because, frankly, neither of those things are true.
For my part? If I'm pressed in the moment and I make a mistake, and that mistake will have repercussions, I just own the mistake when it is brought to my attention or when I realize it on my own, express regret, and introduce retroactive continuity as necessary. It's just a game. I'm not perfect, I don't run a perfect game, and no one expects me to be or do either. No one should expect anyone to. It's unreasonable and unhealthy.
If a player is pressuring a dungeon master to never make mistakes, that's a good example of bad, unhelpful stress that the dungeon master should remove from their life. On the other hand, the stress a dungeon master feels when required to worldbuild under pressure is
not bad stress; it's the same stress you feel at the gym, or while completing a chemistry lab in school. It's the body's way of telling us it is learning.
Again, I'm not saying don't use random generators, I'm just saying that they can absolutely force worldbuilding that reduces player fun, or that isn't consistent with established canon, just like rushed DM fiat can. It doesn't solve the problems you propose. The best reason to use random generators is because you like random results -- as
@dave2008 puts it, if you like not knowing. They can't do anything else better than your brain can.