America needs a new political party. Both of the current ones are bad. Republicans are way too reactionary, Democrats are pro-censorship, and both are getting more extreme. Neither appropriately represents an average person.
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Look up how a vote of no confidence works in the UK and many other parliamentary democracies. Trusting the president to make “the right choices” is simply not an adequate solution for a country. If the people no longer wish for a president to be in office, especially if his own party no longer supports him, he should be removed. It’s about increasing accountability and it works. Look how Liz Truss and Boris Johnson were easily replaced with a (slightly) more competent person. It means that there is no way for a politician to do anything that doesn’t align with what he promised to voters and what his party stands for 
I don’t think following the steps of the UK is a good idea considering its politics is an absolute shitshow. A party in power that knows that the populace despises it choosing a PM on their own volition is inheritably undemocratic.
What? That’s the most democratic thing that can be. There, a political party is a collection of the people, who form a group around a set of shared ideals. Members of a political party usually share opinions on the vast majority of issues, unlike in the U.S. which only has two parties. In the two-party system, there is less infighting/arguing by politicians of the same party, and more cooperation. Because the parliament/congress can also be voted out at any moment, the people truly control the politicians at both the lawmaking and executive branches.
The Conservative Party of the UK has 54% of the seats in Parliament despite having a 20 percentage point deficit in the polls behind Labour, and yet they got to decide the next PM by themselves without having to conduct a general election.
Okay, same thing that happens in the US in that regard. But within the conservative party, decisions can be made that actually reflect what’s best for the country/what the members of the party want. You can see that with Liz Truss and Boris Johnson, who were both basically destroying the country. In the U.S., someone like George Santos could even become president, and, because he’s also controlled by corporations, he doesn’t have to keep any of his campaign promises to the people and he can do whatever the corporations tell him too.
You’re vastly overestimating the amount of corruption in the US; the Corruption Perceptions Index places it at 24th between Austria and Taiwan. Also, in an ideal system, Johnson and Truss wouldn’t have become PMs in the first place.
They promised some ideals that were appealing to voters, and didn’t deliver on them. But the point is that systems need to be put in place to improve a country’s democratic function when this does happen.
About the corruption,
"Nearly 20% of Congress members have been trading shares of companies in industries they are supposed to be overseeing as part of their committee assignments — creating major conflicts of interest, a new report finds." (Source: NYPost, NYTimes).
Sources:
https://www.nytimes.com/interactive/2022/09/13/us/politics/congress-members-stock-trading-list.html
especially if his own party no longer supports him
No, only the people should make that choice
The people are making that choice, as the party is an organization of the people who vote within the part for what the party stands for. Because there are many political parties, a party is more of a set of ideals, rather than a group of people who practically agree on nothing (like in the U.S.). Also, because there is voting within a party, it means that the representatives chosen by the party actually fit a set of specific ideas (not a garbled mess of arguing and infighting like in the two-party system). A party should be a unified group that pushes one idea.