The flaw lies in your Constitution, I'm afraid. I've been through it a couple of times, and have noticed several things.
Firstly, that it was written by businessmen, and as such, is designed to place as little restriction as possible on business.
Secondly, it was written by and for an elite who never expected the common man, (much less women , Black people, Naitive Americans etc) to gain or use the vote.
Thirdly, the assumption that those who entered Congress would always be in general agreement with each other about how things should be done, what should be done and when. Because they would all be men of similar background and interests, from the same social class. The idea of party politics was in its infancy back then, with the only real difference being between rural agricultural interests and urban mercantile ones. Since these were interdependent in many ways, consensus was generally achievable. The framers could not have imagined the current party system and it's increasing polarisation.
Fourthly, all raised under monarchies, the framers never considered the concept of an apolitical, purely ceremonial, Head of State. The separation of executive from legislature has proved increasingly problematic. Because the President is outside Congress, and possesses such wide powers, they are unaccountable. Also, it is too often the case that Presidents are not members of the majority in Congress, which can effectively paralyse government.
The system over here in the UK is in no way perfect. However, the requirement for the Prime Minster and their Cabinet to be Members of Parliament at least allows them to be held to account and be forced to justify their actions and policies to the House. I cannot imagine either Trump or Biden surviving one session of Prime Ministers' Questions! Rishi Sunak is brighter than the pair of them put together, and he struggles at times!
That is one change that direly needs to be made. The office of President should be stripped of all non-ceremonial functions except for the pro forma signing of Bills into law. The executive needs to be part of the legislature (preferably the lower house), directly answerable to members. Also, the requirement for passing of bills needs to be a simple majority.
It need hardly be said that much would be gained by state funding of campaigns. One thing being the chance for other parties to compete for votes on more equal terms.
