That breaks down when you take into account gerrymandering. The politicians in essence do elect themselves when they create with scientific precision these spiney ink blobs of voting districts. The people don't choose their politician, the politicians choose their voters. The more they win the more they can gerrymander as the winners create the districts. This creates an environment where they are not afraid of losing their seat to the other side but instead the threat is being displaced in your own party, driving ever more extreme positions.