That's the clever bit of the US form of governance.
You can have an idiot in the White and the Senate and Congress just get on with running the country.
And the downside is that nobody can be held responsible for anything, because they can all point to someone else and say "don't blame me, it's all the fault of the other guy because he didn't do his part".
When Britain introduced elected government into Canada, do you know what they called it? Lord Durham called it "responsible government". It was called "responsible" because there was to be no question about who was to be held responsible and accountable for the government's performance (I won't go into the history of the crony capitalism system it was replacing). The cabinet is responsible directly to parliament, and parliament is held responsible by the voters. If something goes wrong, there's no question about who is responsible for it. Toss the government out via an election and put in a new one. Is there a deadlock in parliament? Call an election and let the voters sort it out with a new parliament. The House of Commons won't pass the government's budget? Call an election (on a confidence measure) and let the voters sort it out.
The US government is a typical product of 18th century social engineering theory. Social philosophers were fascinated by the machines of the new industrial age and saw society as a machine, with political institutions acting as the gears and levers of a social machine. The perfect society was to be produced by social engineering, with the political institutions acting as the engine.
It's the same sort of thought process which eventually led to Marxism, which was to produce a "new socialist man" by tinkering with the material conditions of society. That's not to imply that there is a link leading from US political ideology to Marxism, but rather both were the product of the idea of society being capable of being consciously engineered.
The parliaments which serve Britain, Canada, Australia, New Zealand, and others are on the other hand the product of a sort of Darwinian evolution. Nobody "designed" it, but it exists because it works, and has evolved over time to suit changing circumstances. What it has going for it more than anything else is that it is simple and direct, and there's no question about who is to be held responsible for what.
I don't think the US "engineered system" can be changed at this point. It's too deeply ingrained into their political consciousness. However, it's not what I would select if I were given a choice.