With great power comes great responsibility. If the most powerful person in the world doesn't bear ultimate responsibility when the party he controls can't fund the government he runs, who else is responsible? It doesn't matter he's not a dictator, he's POTUS, he's the leader. The throne comes equipped with a sword dangling above it.
Past presidents understood assuming ultimate responsibility is in the job description, and voters understand it as well. Maybe you think it's incredibly stupid, but I think it's a hallmark of a great leader to assume ultimate responsibility, especially when negative outcomes are not in his control. Conversely, I think weak, feckless leaders pass the buck to subordinates and/or opponents.
Past presidents tried their best to weasel their way out of any responsibility for things going wrong and blame the other side for everything. That's being a politician. The only difference is that the power levels on Trump's reality distortion field are miles past what anyone thought possible in 2015.
They do think that, but it's an incredibly stupid way to think about the US government. The president isn't a dictator.