You could just have a representative democracy or similar with a system which is known to be broken on a fundamental level.

Like some European countries have democratic systems which allow for a proper versatility of possible parties and the chance for new parties to be created all the times. The US on the other hand has a systems which will always converge to a two party system without any chance for any new parties. At the same time that your choice to choose your representative is massively restricted. There are a bunch of possible systems to allow a this without leading to too much fragmentation.

Then there is the problem with how the "winner takes it all" is applied even before the final result is reached, there might be historical technical reasons for it but today there is no reason why any persons vote should count more then another persons vote (like it's in the US indirectly through there electors system).

Then normally there should be local results given on somewhat natural zoning like cities, normal city districts or not absurdly cut area codes. But in the US this is not the case instead the zone are redone frequently and while this can be done in the interest of the public it's to often used to remove the voting power from local minorities (Gerrymandering).

Then there is the think about the president seemingly being elected directly but that actually not being the case as the vote goes through electors, which basically can just change it. Even just a single elector abusing his/her power would cause a insane amount of votes to be flipped to the exact opposite. While this has historical technical reasons (which probably made sense back then) by now it serves no purpose except that if it's ever abused it will cause instability and potential civil unrest if it changes the end result of a presidential election.

There is also a problem with the US ID system (like there is non) which can cause people problems when they want to vote, but I guess it might not matter to much, maybe??

Also the US president has IMHO to much power. As far as I understand the US system the president was never meant to hold to much power but and orginally didn't hold much power but by now is holding practically quite a bit more power. Through in difference to what is often believed outside of the US the US president doesn't have the complete power at all. Even through Trump said so at least on time.

There are also problems with the US "check & balances" system but I don't remember them. Basically executive, juriscrative and legislative power should keep each other in balance but don't do so well. Btw. this is a problem which isn't too uncommon in democracies.

This is sadly not a complete list of problems with US democracy and IMHO the main problem is still the way the system forces a two party system. Also it's not that other democracies don't have their own problems, they do. But I feel that the US need to improve on it's system or it might run into problems in the near future, I hope it's not to late. But then I guess they won't change anything until they hit a wall.

(Also there are some representative democracies with elements of direct democracies which work just fine.)