Congress could, in theory, begin an arduous process (weeks? months?) in which eventually, if they succeed, again in theory it removes the President and... puts in his place his chosen replacement. It has never successfully done this, so from there we're in uncharted waters but it's hardly obvious that it is an effective procedure.
In contrast the Westminster Parliament routinely disposes of Prime Ministers who lose its confidence, it's already happened once in my lifetime and it's not some multi-week procedure in which there's some performance of a judicial process, just a simple question: Does this Government retain the Confidence of the House?
Margaret Thatcher decided on this course of action on a Monday, on Wednesday morning she rose to say, "Mr. Speaker, I beg to move, 'That this House has no confidence in Her Majesty's Government.'" and by the next morning the Callaghan minority government had fallen.
The length of time the process takes is entirely under the control of Congress. It could be done in a day if they wanted. The longer time periods seen with Clinton and Trump were to attempt to gin up the political support to follow through.
I was concerned with facts, whereas you seem focused on a fantasy about how you wish things were. But your fantasy doesn't matter at all. US-style Presidential Republics are a known bad design, the US nation building projects stopped doing this themselves because it doesn't work, the United States itself is just a slower decay, it's not an exception.
The problem wasn't the Crown, that's the big takeaway. Giving the same power to a guy who doesn't have a hat doesn't fix the problem. You need to hold this much power in commission, that's the lesson that gave us the present British arrangement - the Lord High Treasurer was much too powerful, so his power was given to a commission, today its First Lord though not nearly as powerful as the Lord Treasurer, is too powerful, that's the Prime Minister you gestured at - the formal office is "First Lord of the Treasury", with the Chancellor being Second Lord, and the whips taking subsidiary parts of the commission. If you ask me we should further re-divide this power.
But just giving all that power to one man (and in the US it has always been a man) is even worse. The US President has powers that a King had, which made sense in the 18th century but stands out today - that's why Trump can corruptly pardon people for example.
It's really baffling to see this take repeated, especially when we've seen European PMs rewrite their country's constitution. That's just not feasible in the US system. US Presidents are quite limited in their power. A lot of (justified) outrage occurs over the US President doing something that PMs can typically do with no issue.
You seem fixated on the practical process of removing one from power, which is of course irrelevant as long as their party backs them, which is the actual threat in both cases. In either case, if the legislature does not back them, they can be removed from power with little issue.
I see in a sibling comment you think this is actually a weakness of the US system...apparently the PM radically changing all the laws, norms, and unwritten constitution of his country is "not powerful", while the US President typically fighting a battle to get one single major piece of legislation through in his career is unitarian dictatorship?
> , the US nation building projects stopped doing this themselves because it doesn't work, the United States itself is just a slower decay, it's not an exception.
The US nation building projects felt that parliamentary democracies were easier to control, as direct election of Presidential executives sometimes leads to democracies electing leaders who are able to carry out policies that violate US interests.
In contrast the Westminster Parliament routinely disposes of Prime Ministers who lose its confidence, it's already happened once in my lifetime and it's not some multi-week procedure in which there's some performance of a judicial process, just a simple question: Does this Government retain the Confidence of the House?
Margaret Thatcher decided on this course of action on a Monday, on Wednesday morning she rose to say, "Mr. Speaker, I beg to move, 'That this House has no confidence in Her Majesty's Government.'" and by the next morning the Callaghan minority government had fallen.