Cheating with elections is so much easier with district voting than proportional representation. The founders of the constitution hated parties but ended up with the game that leaves only a two party competition. That's hardly a choice, it's a single bit.
A real democratic system allows you to grow a political movement naturally over the years to take over and replace corrupt parties peacefully. But district voting system allows two party system to remain in power indefinitely. It completely prevents the entire point of democracy of allowing peaceful transition of power and replacement of corrupt power structures.
There's an additional problem, which is why isn't even harder to replace district voting, that those in charge of counting votes are local to each district, which is letting the car guard the cream.
In proper system with proportional representation, you need to ensure that each location doesn't abuse it's power to count votes and to fabricate population counts to gain an advantage, and you can only do so if you bring random people from different locations to count the votes in each place.