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.
All of that is just a side-effect of a two-party system, not a presidential system as opposed to a parliamentary system.
No, it also has to do with a parliamentary system, as the way in which politicians are held accountable is vastly different. I highly recommend you check out the Wikipedia page for a vote of no confidence. I agree that a multi-party system solves some of these issues in itself, but definitely not all of them. In order to reduce corruption/control of politicians by corporations, you need a more responsive/dynamic system that can react to the current views of the people.
In modern times, the passage of a motion of no confidence is a relatively rare event in two-party democracies. In almost all cases, party discipline is sufficient to allow a majority party to defeat a motion of no confidence, and if faced with possible defections in the government party, the government is likely to change its policies, rather than lose a vote of no confidence. The cases in which a motion of no confidence has passed are generally those in which the government party's slim majority has been eliminated by either by-elections or defections, such as the 1979 vote of no confidence in the Callaghan ministry in the UK which was carried by one vote and forced a general election, which was won by Margaret Thatcher's Conservative Party.
Motions of no confidence are far more common in multi-party systems in which a minority party must form a coalition government. That can mean that there have been many short-lived governments because the party structure allows small parties to defeat a government which does not have the majority needed to create a government. This has widely been regarded as the cause of instability for the French Fourth Republic and the German Weimar Republic. More recent examples have been in Italy between the 1950s and 1990s, Israel, and Japan.
This isn’t quite true, because both Boris and Liz were forced out by the threat of a vote of no confidence because when they saw that one was inevitable, they both resigned. Having this measure in place still affects how politicians behave, but it doesn’t really matter whether they choose to resign or not, as it’s the same outcome anyway.