To be fair, a Republic with a mostly democratic system is far better than the governments available at the time. The entire world was essentially all monarchies.
Now, the issue with the implementation was that initially, only land-owning free white men could vote. Over time, the people who were eligible to vote increased and the barriers to voting were gradually removed due to pressue from the people. The election system in the US today is far better than what it had been.
But here some issues that needs to be fixed:
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Get rid of the electoral college. One-person, one-vote. Electoral college violates that principle.
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Ranked choice voting / Instant runoff to replace first-past-the-post
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Get rid of the Senate, transfer all their powers to the House. Get rid of gerrymandering by allocating seats based on percentage of votes. Getting 51% of the votes means roughly 51% of the seats, not 45% of the seats due to some stupid districting shenanigans.
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Supreme Court justices should not be permanent. Example: 15 seats and each seat has a 15-year term with staggering expiration. Each year would have one seat expiring. Each year, one person will be appointed. If a judge dies before the seat expires, appointment would require 2/3 of the vote to confirm, or wait until the year it's suppose to expire then you can appoint one with only 1/2. One president shouldn't have more influence over others because there happens to be more Supreme Court justice death during the term.
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Get rid of bribery. ~~And Congress members should not be allowed to access their money during the term and live on minimum wage only in the official residence to be provided by the government. (Well they probably shouldn't have that much money at all, but that's a topic for another time) Let's see how quickly rich congresspeople would quit when they don't have access to their luxury lifestyle.~~ (Edit: On a second thought, this part seems a bit problematic. The other points still stand.)
That's some basics on how to make things better. Not perfect, in fact, far from perfect, but more bearable until we can convince people to make more changes.